Which polynomial is a difference of squares?
a. x2 – 16x + 64
b. x2 + 4
c.9x2 – x – 36
d.25x2 – 36

Answer

D.25x2 – 36

Explanation

A. x² – 16x + 64

product = 64

sum = -16

factors: -8 and -8

x² – 16x + 64  = x² - 8x - 8x + 64

                       = x(x - 8) - 8(x - 8)

                        = (x - 8)(x-8) = (x-8)²      ⇒ Not a difference of squares

B.x² + 4 = (x² + 2²) ⇒ Not a difference of squares

C.9x² – x – 36

product = - 324

sum = -1

Factors: none

9x² – x – 36  ⇒ Has no perfect roots.

D.25x² – 36

25x² – 36 = (5x)² - 6²   ⇒ This is the difference of squares.

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