Factor the expression completely. $9 z ^ { 2 } + 42 z + 49$
A) $\quad ( 3 z - 7 ) ^ { 2 }$
B) $\quad ( 3 z + 7 ) ( 3 z - 7 )$
C) $\quad 7 ( 3 z + 7 )$
D) $\quad ( 3 z + 7 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

The expression can be factored using the perfect square trinomial formula, which states that for any trinomial of the form $ax^2+bx+c$ where $a$ is a perfect square, $b=2ak$, and $c=k^2$, the trinomial can be factored as $(\sqrt{a}x+k)^2$. In this case, we can rewrite $9z^2+42z+49$ as $(3z)^2+2\cdot3z\cdot7+7^2$, so the expression is a perfect square trinomial with $a=3^2=9$, $b=2\cdot3\cdot7=42$, and $c=7^2=49$. Therefore, we can factor the expression as $(3z+7)^2$. Choice D is the only option that matches this factorization.

Factor the Expression Completely 9z2+42z+499 z ^ { 2 } + 42 z + 499z2+42z+49

Factor the Expression Completely $9 z ^ { 2 } + 42 z + 49$