Factor by any method.
-Find all values of a that will make the polynomial a perfect square trinomial. $$36 x ^ { 2 } + a x + 25$$
A) 30
B) 60
C) 60, -60
D) 30, -30

Question

Quizplus · Accepted Answer

A perfect square trinomial has the form $(ax)^2 + 2abx + b^2$, where the first term is a square, the last term is a square, and the middle term is twice the product of the square roots of the first and last terms. In this case, the first term is $36x^2$ (where $a = 6x$) and the last term is $25$ (where $b = 5$). To make the polynomial a perfect square trinomial, the middle term $ax$ should equal $2 \cdot 6x \cdot 5 = 60x$. Therefore, $a$ can be $60$. However, considering the formula for a perfect square trinomial can also be applied in the form $(ax)^2 - 2abx + b^2$, $a$ can also be $-60$, making the polynomial $(6x - 5)^2$. Thus, both $60$ and $-60$ are correct.

Factor by Any Method 36x2+ax+2536 x ^ { 2 } + a x + 2536x2+ax+25

Factor by Any Method $36 x ^ { 2 } + a x + 25$