Advertisements
Advertisements
Question
Factorise:
x3 + x2 – 4x – 4
Advertisements
Solution
Let p(x) = x3 + x2 – 4x – 4
Constant term of p(x) = – 4
Factors of – 4 are ±1, ±2, ±4
By trial, we find that p(–1) = 0, so (x + 1) is a factor of p(x)
Now, we see that x3 + x2 – 4x – 4
= x2(x + 1) – 4(x + 1)
= (x + 1)(x2 – 4) ...[Taking (x + 1) common factor]
Now, x2 – 4 = x2 – 22
= (x + 2)(x – 2) ...[Using identity, a2 – b2 = (a – b)(a + b)]
∴ x3 + x2 – 4x – 4 = (x + 1)(x – 2)(x + 2)
APPEARS IN
RELATED QUESTIONS
Write the coefficient of x2 in the following:
`17 -2x + 7x^2`
f(x) = 9x3 − 3x2 + x − 5, g(x) = \[x - \frac{2}{3}\]
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x - \frac{1}{2}\].
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) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
Find α and β, if x + 1 and x + 2 are factors of x3 + 3x2 − 2αx + β.
Find the values of a and b so that (x + 1) and (x − 1) are factors of x4 + ax3 − 3x2 + 2x + b.
What must be subtracted from x3 − 6x2 − 15x + 80 so that the result is exactly divisible by x2 + x − 12?
Using factor theorem, factorize each of the following polynomials:
x3 + 6x2 + 11x + 6
2x4 − 7x3 − 13x2 + 63x − 45
