Question

What is the complete factorization of the polynomial below x^3+x^2+9x+9

Answer 1

Answer: (x+1)(x² + 9)

Explanation:

Let f(x)=x³ + x² + 9x + 9

let x= -1

f(-1) = (-1)³ +(-1)² + 9(-1) + 9

= -1 +1 -9 +9 =0

Therefore, (x+1) is a factor

we now divide x³ + x² + 9x + 9 by x+1

x² + 9

_________

x+ 1√x³ + x² + 9x +9

- (x³ + x²)

______________

9x + 9

- (9x +9)

_______________

0

Therefore, (x+1) and (x² + 9) are the 2 factors of the polynomial.

Answer 2

using factoring by grouping:

(x^3 + x^2) + (9x + 0)

x^2(x+1) + 9(x+1)

(x^2+9)(x+1)