Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $16 m ^ { 2 } + 72 m + 81$
A) $( 4 m - 9 ) ^ { 2 }$
B) $( 4 m + 9 ) ^ { 2 }$
C) $16 ( m + 9 ) ^ { 2 }$
D) Not a perfect square trinomial

Question

Quizplus · Accepted Answer

The greatest common factor (GCF) of the given polynomial $16m^2 + 72m + 81$ is 1, so factoring out the GCF does not change the polynomial. To determine if it's a perfect square trinomial, we look for the form $a^2 + 2ab + b^2 = (a + b)^2$. Here, $16m^2$ is $a^2$ with $a = 4m$, and $81$ is $b^2$ with $b = 9$. The middle term, $72m$, is $2ab = 2(4m)(9) = 72m$, which matches the given polynomial. Therefore, the polynomial is a perfect square trinomial and factors to $(4m + 9)^2$.

Factor Out the Greatest Common Factor 16m2+72m+8116 m ^ { 2 } + 72 m + 8116m2+72m+81

Factor Out the Greatest Common Factor $16 m ^ { 2 } + 72 m + 81$