Factor by any method.
-Find all values of a that will make the polynomial a perfect square trinomial. $$4 x ^ { 2 } + a x + 16$$
A) $16 , - 16$
B) 16
C) 8
D) $8 , - 8$

Question

Quizplus · Accepted Answer

For a trinomial to be a perfect square, it must be in the form $(mx + n)^2 = m^2x^2 + 2mnx + n^2$. Comparing this with the given polynomial $4x^2 + ax + 16$, we see that $m^2 = 4$ and $n^2 = 16$, so $m = 2$ and $n = 4$. For the middle term, $2mn = a$, so $2 \cdot 2 \cdot 4 = 16$ or $2 \cdot 2 \cdot (-4) = -16$. Therefore, $a$ can be $16$ or $-16$.

Factor by Any Method 4x2+ax+164 x ^ { 2 } + a x + 164x2+ax+16

Factor by Any Method $4 x ^ { 2 } + a x + 16$