Which of the following quadratic expressions is factorable over the integers? Select all that apply from the following. Show your work.
a) x^2 -6x +36
b) x^2 -10x +25
c) 4x^2 + 12x +9
d) 16x^2 + 36x +81
d) 4x^2 - 49
a) x^2 - 6x + 36
If we factor x^2 - 6x + 36, we get:
(x-3)(x-3) or (x-3)^2
b) x^2 - 10x + 25
If we factor x^2 - 10x + 25, we get:
(x-5)(x-5) or (x-5)^2
c) 4x^2 + 12x + 9
If we factor 4x^2 + 12x + 9, we get:
(2x+3)(2x+3) or (2x+3)^2
d) 16x^2 + 36x + 81
If we factor 16x^2 + 36x + 81, we get:
(4x+3)(4x+3) or (4x+3)^2
e) 4x^2 - 49
If we factor 4x^2 - 49, we get:
(2x+7)(2x-7) or (2x+7)(2x-7)
Therefore, the factorable quadratic expressions over the integers are a) x^2 - 6x + 36, b) x^2 - 10x + 25, c) 4x^2 + 12x + 9, and d) 16x^2 + 36x + 81.