How do you factor $5 c^{2} + 12 c + 7$ $5c^2 + 12c + 7$ ?

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Answer 1 · 2015-06-30T19:30:01

Use the $a \cdot c$ $a*c$ method of factoring.

$5 c^{2} + 12 c + 7$ $5c^2+12c+7$ is in the form $a x^{2} + b x + c$ $ax^2+bx+c$ , where $a = 5;$ $a=5;$ $b = 12; and$ $b=12; and$ $c = 7$ $c=7$ .

Multiply $a \cdot c$ $a*c$ , and find two factors that when added equal $b$ $b$ .

$a \cdot c = 5 \cdot 7 = 35$ $a*c=5*7=35$

Find two factors of $35$ $35$ that when added equal $12$ $12$ .

$5$ $5$ and $7$ $7$ fit the criteria. $5 + 7 = 12$ $5+7=12$

Rewrite $12 c$ $12c$ as $5 c$ $5c$ and $7 c$ $7c$ .

Rewrite the expression.

$5 c^{2} + 5 c + 7 c + 7$ $5c^2+5c+7c+7$

Divide the expression into two groups.

$(5 c^{2} + 5 c) + (7 c + 7)$ $(5c^2+5c)+(7c+7)$

Factor out the $5 c$ $5c$ from the first group, and the $7$ $7$ from the second group.

$5 c (c + 1) + 7 (c + 1)$ $5c(c+1)+7(c+1)$

Factor out the common term $(c + 1)$ $(c+1)$ .

$(c + 1) (5 c + 7)$ $(c+1)(5c+7)$

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