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Chapters
2: Exponents of Real Numbers
3: Rationalisation
4: Algebraic Identities
5: Factorisation of Algebraic Expressions
▶ 6: Factorisation of Polynomials
7: Linear Equations in Two Variables
8: Co-ordinate Geometry
9: Introduction to Euclid’s Geometry
10: Lines and Angles
11: Triangle and its Angles
12: Congruent Triangles
13: Quadrilaterals
14: Areas of Parallelograms and Triangles
15: Circles
16: Constructions
17: Heron’s Formula
18: Surface Areas and Volume of a Cuboid and Cube
19: Surface Areas and Volume of a Circular Cylinder
20: Surface Areas and Volume of A Right Circular Cone
21: Surface Areas and Volume of a Sphere
22: Tabular Representation of Statistical Data
23: Graphical Representation of Statistical Data
24: Measures of Central Tendency
25: Probability
![RD Sharma solutions for Mathematics [English] Class 9 chapter 6 - Factorisation of Polynomials - Shaalaa.com](/images/8193647912-mathematics-english-class-9_6:1a030933ece146238cec338f12706a07.jpg "RD Sharma solutions for Mathematics [English] Class 9 chapter 6 - Factorisation of Polynomials")
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Solutions for Chapter 6: Factorisation of Polynomials
Below listed, you can find solutions for Chapter 6 of CBSE RD Sharma for Mathematics [English] Class 9.
RD Sharma solutions for Mathematics [English] Class 9 6 Factorisation of Polynomials Exercise 6.1 [Pages 2 - 3]
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:
3x2 - 4x +15
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:
`y^2 +2sqrt3`
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:
`3sqrtx+sqrt2x`
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:
`x - 4/x`
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:
`x^12+y^3+t^50`
Write the coefficient of x2 in the following:
`17 -2x + 7x^2`
Write the coefficient of x2 in the following:
`9-12x +X^3`
Write the coefficient of x2 in the following:
`pi/6x^2- 3x+4`
Write the coefficient of x2 in the following:
`sqrt3x-7`
Write the degrees of each of the following polynomials
`7x3 + 4x2 – 3x + 12`
Write the degrees of the following polynomials:
`12-x+2x^3`
Write the degrees of the following polynomials:
`5y-sqrt2`
Write the degrees of the following polynomials:
7
Write the degrees of the following polynomials
0
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
`x+x^2 +4`
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
`3x-2`
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
`2x+x^2`
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
`3y`
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
`t^2+1`
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials
`7t^4+4t^3+3t-2`
Classify the following polynomials as polynomials in one-variable, two variables etc:
`x^2-xy+7y^2`
Classify the following polynomials as polynomials in one-variable, two variables etc:
`x^2-2tx+7t^2-x+t`
Classify the following polynomials as polynomials in one-variable, two variables etc:
`t^3_3t^2+4t-5`
Classify the following polynomials as polynomials in one-variable, two variables etc:
`xy+yx+zx`
Identify polynomials in the following:
`f(x)=4x^3-x^2-3x+7`
Identify polynomials in the following:
`g(x)=2x^3-3x^2+sqrtx-1`
Identify polynomials in the following:
`p(x)=2/3x^3-7/4x+9`
Identify polynomials in the following:
`q(x)=2x^2-3x+4/x+2`
Identify polynomials in the following:
`h(x)=x^4-x^(3/2)+x-1`
Identify polynomials in the following:
`f(x)=2+3/x+4x`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`f(x)=0`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`g(x)=2x^3-7x+4`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`h(x)=-3x+1/2`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials
`p(x)=2x^2-x+4`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`q(x)=4x+3`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`r(x)=3x^2+4x^2+5x-7`
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
RD Sharma solutions for Mathematics [English] Class 9 6 Factorisation of Polynomials Exercise 6.2 [Page 8]
If `f(x) = 2x^2 - 13x^2 + 17x + 12` find f(2)
If `f(x)=2x^2-13x^2+17x+12` find `f-(3)`
If `f(x)=2x^2-13x^2+17x+12` find `f(0)`
Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:
`f ( x ) = 3x +1, x = - 1/3`
Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:
`f(x)=x^2- 1,x=1,-1`
Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:
`g(x)=3x^2-2,` `x=2/sqrt3 2/sqrt3`
Verify whether the indicated numbers is zeros of the polynomials corresponding to them in the following case:
\[p(x) = x^3 - 6 x^2 + 11x - 6, x = 1, 2, 3\]
Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:
`f ( x ) = 5x - pi , x = 4/5`
Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:
`f ( x) = x^2and x = 0`
Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:
`f(x) = lx + m , x = - m/1`
Verify whether the indicated numbers is zeroes of the polynomials corresponding to them in the following case:
`f (x) = 2x +1, x = 1/2`
If `x = 2` is a root of the polynomial `f(x) = 2x2 – 3x + 7a` find the value of a.
If `x = −1/2` is a zero of the polynomial `p(x)=8x^3-ax^2 -+2` find the value of a.
If x = 0 and x = −1 are the roots of the polynomial f(x) =2x3 − 3x2 + ax + b, find the value of a and b.
Find the integral roots of the polynomial f(x) = x3 + 6x2 + 11x + 6.
Find rational roots of the polynomial f(x) = 2x3 + x2 − 7x − 6.
RD Sharma solutions for Mathematics [English] Class 9 6 Factorisation of Polynomials Exercise 6.3 [Pages 14 - 15]
In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the result by actual division: (1−8)
f(x) = x3 + 4x2 − 3x + 10, g(x) = x + 4
f(x) = 4x4 − 3x3 − 2x2 + x − 7, g(x) = x − 1
f(x) = 2x4 − 6x3 + 2x2 − x + 2, g(x) = x + 2
f(x) = 4x3 − 12x2 + 14x − 3, g(x) 2x − 1
f(x) = x3 − 6x2 + 2x − 4, g(x) = 1 − 2x
f(x) = x4 − 3x2 + 4, g(x) = x − 2
f(x) = 9x3 − 3x2 + x − 5, g(x) = \[x - \frac{2}{3}\]
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
If the polynomials 2x3 + ax2 + 3x − 5 and x3 + x2 − 4x +a leave the same remainder when divided by x −2, find the value of a.
If the polynomials ax3 + 3x2 − 13 and 2x3 − 5x + a, when divided by (x − 2) leave the same remainder, find the value of a.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x - \frac{1}{2}\].
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x + \pi\] .
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x .
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the value of the following case, if R1 = R2.
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the values of the following case, if R1 + R2 = 0.
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the values of the following cases, if 2R1 − R2 = 0.
RD Sharma solutions for Mathematics [English] Class 9 6 Factorisation of Polynomials Exercise 6.4 [Pages 24 - 25]
In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not: (1−7)
f(x) = x3 − 6x2 + 11x − 6; g(x) = x − 3
f(x) = 3x4 + 17x3 + 9x2 − 7x − 10; g(x) = x + 5
f(x) = x5 + 3x4 − x3 − 3x2 + 5x + 15, g(x) = x + 3
f(x) = x3 −6x2 − 19x + 84, g(x) = x − 7
f(x) = 3x3 + x2 − 20x +12, g(x) = 3x − 2
f(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
f(x) = x3 − 6x2 + 11x − 6, g(x) = x2 − 3x + 2
Show that (x − 2), (x + 3) and (x − 4) are factors of x3 − 3x2 − 10x + 24.
Show that (x + 4) , (x − 3) and (x − 7) are factors of x3 − 6x2 − 19x + 84
For what value of a is (x − 5) a factor of x3 − 3x2 + ax − 10?
Find the value of a such that (x − 4) is a factors of 5x3 − 7x2 − ax − 28.
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
Find the value k if x − 3 is a factor of k2x3 − kx2 + 3kx − k.
Find the values of a and b, if x2 − 4 is a factor of ax4 + 2x3 − 3x2 + bx − 4.
Find α and β, if x + 1 and x + 2 are factors of x3 + 3x2 − 2αx + β.
If x − 2 is a factor of the following two polynomials, find the values of a in each case x3 − 2ax2 + ax − 1.
If x − 2 is a factor of the following two polynomials, find the values of a in each case x5 − 3x4 − ax3 + 3ax2 + 2ax + 4.
In the following two polynomials, find the value of a, if x − a is factor x6 − ax5 + x4 − ax3 + 3x − a + 2.
In the following two polynomials, find the value of a, if x − a is factor (x5 − a2x3 + 2x + a + 1).
In the following two polynomials, find the value of a, if x + a is a factor x3 + ax2 − 2x +a + 4.
In the following two polynomials, find the value of a, if x + a is a factor x4 − a2x2 + 3x −a.
Find the values of p and q so that x4 + px3 + 2x3 − 3x + q is divisible by (x2 − 1).
Find the values of a and b so that (x + 1) and (x − 1) are factors of x4 + ax3 − 3x2 + 2x + b.
If x3 + ax2 − bx+ 10 is divisible by x2 − 3x + 2, find the values of a and b.
If both x + 1 and x − 1 are factors of ax3 + x2 − 2x + b, find the values of a and b.
What must be added to x3 − 3x2 − 12x + 19 so that the result is exactly divisibly by x2 + x - 6 ?
What must be subtracted from x3 − 6x2 − 15x + 80 so that the result is exactly divisible by x2 + x − 12?
What must be added to 3x3 + x2 − 22x + 9 so that the result is exactly divisible by 3x2 + 7x − 6?
RD Sharma solutions for Mathematics [English] Class 9 6 Factorisation of Polynomials Exercise 6.5 [Pages 32 - 33]
Using factor theorem, factorize each of the following polynomials:
x3 + 6x2 + 11x + 6
x3 + 2x2 − x − 2
x3 − 6x2 + 3x + 10
x4 − 7x3 + 9x2 + 7x − 10
3x3 − x2 − 3x + 1
x3 − 23x2 + 142x − 120
y3 − 7y + 6
x3 − 10x2 − 53x − 42
y3 − 2y2 − 29y − 42
2y3 − 5y2 − 19y + 42
x3 + 13x2 + 32x + 20
x3 − 3x2 − 9x − 5
2y3 + y2 − 2y − 1
x3 − 2x2 − x + 2
Factorize of the following polynomials:
x3 + 13x2 + 31x − 45 given that x + 9 is a factor
Factorize of the following polynomials:
4x3 + 20x2 + 33x + 18 given that 2x + 3 is a factor.
x4 − 2x3 − 7x2 + 8x + 12
x4 + 10x3 + 35x2 + 50x + 24
2x4 − 7x3 − 13x2 + 63x − 45
RD Sharma solutions for Mathematics [English] Class 9 6 Factorisation of Polynomials Exercise 6.6 [Pages 33 - 34]
Define zero or root of a polynomial.
If \[x = \frac{1}{2}\] is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.
Write the remainder when the polynomialf(x) = x3 + x2 − 3x + 2 is divided by x + 1.
Find the remainder when x3 + 4x2 + 4x − 3 is divided by x.
If x + 1 is a factor of x3 + a, then write the value of a.
If f(x) = x4 − 2x3 + 3x2 − ax − b when divided by x − 1, the remainder is 6, then find the value of a + b
RD Sharma solutions for Mathematics [English] Class 9 6 Factorisation of Polynomials Exercise 6.7 [Pages 34 - 35]
Mark the correct alternative in each of the following:
If x − 2 is a factor of x2 + 3ax − 2a, then a =
2
-2
1
-1
If x3 + 6x2 + 4x + k is exactly divisible by x + 2, then k =
−6
−7
−8
−10
If x − a is a factor of x3 −3x2a + 2a2x + b, then the value of b is
0
2
1
3
If x140 + 2x151 + k is divisible by x + 1, then the value of k is
1
-3
2
-2
If x + 2 is a factor of x2 + mx + 14, then m =
7
2
9
14
If x − 3 is a factor of x2 − ax − 15, then a =
-2
5
-5
3
If x51 + 51 is divided by x + 1, the remainder is
0
1
49
50
If x + 1 is a factor of the polynomial 2x2 + kx, then k =
-2
-3
4
2
If x + a is a factor of x4 − a2x2 + 3x − 6a, then a =
0
-1
1
2
The value of k for which x − 1 is a factor of 4x3 + 3x2 − 4x + k, is
3
1
-2
-3
If x + 2 and x − 1 are the factors of x3 + 10x2 + mx + n, then the values of m and n are respectively
5 and −3
17 and −8
7 and −18
23 and −19
Let f(x) be a polynomial such that \[f\left( - \frac{1}{2} \right)\] = 0, then a factor of f(x) is
2x − 1
2x + 1
x − 1
x +1
When x3 − 2x2 + ax − b is divided by x2 − 2x − 3, the remainder is x − 6. The values of a and b are respectively
−2, −6
2 and −6
- 2 and 6
2 and 6
One factor of x4 + x2 − 20 is x2 + 5. The other factor is
x2 − 4
x − 4
x2 − 5
x + 2
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
f(x) g(x)
−f(x) + g(x)
f(x) − g(x)
\[\left\{ f(x) + g(x) \right\} g(x)\]
(x+1) is a factor of xn + 1 only if
n is an odd integer
n is an even integer
n is a negative integer
n is a positive integer
If x2 + x + 1 is a factor of the polynomial 3x3 + 8x2 + 8x + 3 + 5k, then the value of k is
0
2/5
5/2
-1
If (3x − 1)7 = a7x7 + a6x6 + a5x5 +...+ a1x + a0, then a7 + a5 + ...+a1 + a0 =
0
1
128
64
If both x − 2 and \[x - \frac{1}{2}\] are factors of px2 + 5x + r, then
p = r
p + r = 0
2p + r = 0
p + 2r = 0
If x2 − 1 is a factor of ax4 + bx3 + cx2 + dx + e, then
a + c + e = b + d
a + b +e = c + d
a + b + c = d + e
b + c + d = a + e
Solutions for 6: Factorisation of Polynomials
RD Sharma solutions for Mathematics [English] Class 9 chapter 6 - Factorisation of Polynomials
Shaalaa.com has the CBSE Mathematics Mathematics [English] Class 9 CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. RD Sharma solutions for Mathematics Mathematics [English] Class 9 CBSE 6 (Factorisation of Polynomials) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
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Concepts covered in Mathematics [English] Class 9 chapter 6 Factorisation of Polynomials are Algebraic Identities, Polynomials, Polynomials in One Variable, Zeroes of a Polynomial, Remainder Theorem, Factorisation of Polynomials, Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0..
Using RD Sharma Mathematics [English] Class 9 solutions Factorisation of Polynomials exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in RD Sharma Solutions are essential questions that can be asked in the final exam. Maximum CBSE Mathematics [English] Class 9 students prefer RD Sharma Textbook Solutions to score more in exams.
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