Question

Factors for the polynomial 4x³+ 4x²– 9x – 9 are​

Answer 1

Answer:

(a+b)(a-b)

Step-by-step explanation:

Let us assume x=−1 be the one of the zeroes of the given polynomial,

Given, f(x)=4x

3

+4x

2

–9x–9

Now, substitute the value of x in f(x),

f(−1)=4(−1)3+4(−1)2–9(−1)–9

=−4+4+9–9

=0

Therefore, x+1 is the factor of 4x

3

+4x

2

–9x–9.

Now, dividing 4x

3

+4x

2

–9x–9 by x+1 we get,

REF image:

Therefore, 4x

3

+4x

2

–9x–9=(x+1)(4x

2

–9)

=(x+1)((2x)

2

–(3)

2

)

=(x+1)(2x+3)(2x–3) {using the identity a

2

−b

2

=(a+b)(a−b)}

Answer 2

Answer

4x³+ 4x²– 9x – 9 = (x+1) (2x-3) (2x+3)

roots are -1, 3/2 , -3/2