Factor the following perfect square trinomial. $c ^ { 2 } + 14 c + 49$
A) $( c - 7 ) ^ { 2 }$
B) $( c + 6 ) ^ { 2 }$
C) $( c + 14 ) ^ { 2 }$
D) $( c + 7 ) ^ { 2 }$
E)none of these

Question

Quizplus · Accepted Answer

This trinomial can be factored as $(c+7)^2$ because it follows the pattern of a perfect square trinomial $(a+b)^2 = a^2 + 2ab + b^2$. Specifically, we have $a = c$ and $b = 7$, so $a^2 + 2ab + b^2 = c^2 + 14c + 49$. Thus, the correct choice is (D).

Factor the Following Perfect Square Trinomial c2+14c+49c ^ { 2 } + 14 c + 49c2+14c+49

Factor the Following Perfect Square Trinomial $c ^ { 2 } + 14 c + 49$