Question

use the factor theorem to factorise x3+x2-4x-4

Answer 1

Answer:

(x+1),(x+2) and (x-2) are factors of given polynomial.

Step-by-step explanation:

Given x³+x²-4x-4

= x²(x+1)-4(x+1)

= (x+1)(x²-4)

= (x+1)(x²-2²)

= (x+1)(x+2)(x-2)

/* By algebraic identity:

a²-b² = (a+b)(a-b) */

Therefore,

(x+1),(x+2) and (x-2) are factors of given polynomial.

•••♪

Answer 2

Step-by-step explanation:

Let f(x)=x

3

+x

2

–4x–4

For x=−1, the value of f(x) will be

f(−1)=(−1)

3

+(−1)

2

–4(−1)–4

=−1+1+4–4=0

As, f(−1)=0 so (x+1) is a factor of f(x).

Now, performing long division we have

Thus, f(x)=(x+1)(x

2

–4)

=(x+1)(x–2)(x+2)