Question

Factor this polynomial expression. X^2 + 8x + 16

Answer 1

Answer:

D. (x + 4)(x + 4)

Step-by-step explanation:

The poynomial x^2 + 8x + 16 is a perfect trinomial.

Perfect trinomials are when the square root of the first term, multiplied by the square root of the third term, multiplied by 2, is equal to the middle term.

In trinomial ax² + bx + c, it is perfect when:

(2) (√(ax²)) (√c) = bx

In x² + 8x + 16,

2(√x²)(√16) = 8x

The formula for a perfect trinomial is:

ax² ± bx + c   =  (√(ax²) ± √c)(√(ax²) ± √c)   =  (√(ax²) ± √c)²

Open up two brackets. Square the first and last term, and they are either added or subtracted based on the sign before the middle term.

In x² + 8x + 16,

(√x² + √16)² = (x + 4)² = (x + 4)(x + 4)