Advertisements
Advertisements
Question
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
Solution
x3 + x2 - 4x - 4
Let x + 1 = 0
∴ x = -1
On substituting value of x in the expression
∴ f(-1) = (-1)3 + (-1)2 - 4(-1) -4 = 0
Clearly x + 1 is a factor of
f(x) = x3 + x2 - 4x - 4
∴ f(x) = (x + 1) (x2 - 4) ...(By actual division)
= (x + 1) (x - 2) (x + 2)
APPEARS IN
RELATED QUESTIONS
Using the Factor Theorem, show that (x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1)
Show that m − 1 is a factor of m21 − 1 and m22 − 1.
If x - 2 and `x - 1/2` both are the factors of the polynomial nx2 − 5x + m, then show that m = n = 2
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2)
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5.
Show that 2x + 7 is a factor of 2x3 + 5x2 - 11 x - 14. Hence factorise the given expression completely, using the factor theorem.
Show that 2x + 7 is a factor of 2x3 + 5x2 – 11x – 14. Hence factorise the given expression completely, using the factor theorem.
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
