Advertisements
Advertisements
प्रश्न
Use factor theorem to factorise the following polynomials completely: 4x3 + 4x2 – 9x – 9
उत्तर
f(x) = 4x3 + 4x2 – 9x – 9
Let x = -1, then
f(-1) = 4 (-1)3 + 4 (-1)2 – 9 (-1) – 9
= 4(–1) + 4(1) + 9 – 9
= –4 + 4 + 9 – 9
= 13 – 13
= 0
∴ (x + 1) is a factor of f(x)
Now dividing f(x) by x + 1, we get
f(x) = 4x3 + 4x2 – 9x – 9
= (x + 1)(4x2 – 9)
= (x + 1){(2x)2 – (3)2}
= (x + 1)(2x + 3)(2x – 3)
`x + 1")"overline(4x^3 + 4x^2 - 9x - 9)("4x^2 - 9`
4x3 + 4x2
– –
– 9x – 9
– 9x – 9
+ +
x
APPEARS IN
संबंधित प्रश्न
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.
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.
The polynomial px3 + 4x2 – 3x + q is completely divisible by x2 – 1; find the values of p and q. Also, for these values of p and q, factorize the given polynomial completely.
Show that x2 - 9 is factor of x3 + 5x2 - 9x - 45.
Factorize completely using factor theorem:
2x3 – x2 – 13x – 6
While factorizing a given polynomial, using remainder and factor theorem, a student finds that (2x + 1) is a factor of 2x3 + 7x2 + 2x – 3.
- Is the student's solution correct stating that (2x + 1) is a factor of the given polynomial?
- Give a valid reason for your answer.
Also, factorize the given polynomial completely.
If (x – a) is a factor of x3 – ax2 + x + 5; the value of a is ______.
