Advertisements
Advertisements
प्रश्न
Factorise x3 + 6x2 + 11x + 6 completely using factor theorem.
उत्तर
Let f(x) = x3 + 6x2 + 11x + 6
For x = –1
f(–1) = (–1)3 + 6(–1)2 + 11(–1) + 6
= –1 + 6 – 11 + 6
= 12 – 12
= 0
Hence, (x + 1) is a factor of f(x).
x2 + 5x + 6
`x + 1")"overline(x^3 + 6x^2 + 11x + 6)`
x3 + x2
5x2 + 11x
5x2 + 5x
6x + 6
6x + 6
0
∴ x3 + 6x2 + 11x + 6 = (x + 1)(x2 + 5x + 6)
= (x + 1)(x2 + 2x + 3x + 6)
= (x + 1)[x(x + 2) + 3(x + 2)]
= (x + 1)(x + 2)(x + 3)
APPEARS IN
संबंधित प्रश्न
Factorise the expression f(x) = 2x3 – 7x2 – 3x + 18. Hence, find all possible values of x for which f(x) = 0.
Given that x – 2 and x + 1 are factors of f(x) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
Using remainder Theorem, factorise:
2x3 + 7x2 − 8x – 28 Completely
Using the Reminder Theorem, factorise of the following completely.
2x3 + x2 – 13x + 6
Find the values of a and b in the polynomial f(x) = 2x3 + ax2 + bx + 10, if it is exactly divisible by (x+2) and (2x-1).
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x4 - a2x2 + 3x - a.
If (x – 2) is a factor of 2x3 – x2 + px – 2, then
(i) find the value of p.
(ii) with this value of p, factorise the above expression completely
If x3 – 2x2 + px + q has a factor (x + 2) and leaves a remainder 9, when divided by (x + 1), find the values of p and q. With these values of p and q, factorize the given polynomial completely.
If (x + 3) and (x – 4) are factors of x3 + ax2 – bx + 24, find the values of a and b: With these values of a and b, factorise the given expression.
