How do you factor completely: $5x^2 − 2x − 7$ ?

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Answer 1 · 2015-07-20T03:15:09

$5x^2-2x-7=(5x-7)(x+1)$

$5x^2-2x-7$ is a quadratic equation in the form $ax^2+bx+c$ , in which $a=5, b=-2, and c=-7$ .

This equation can be factored by the $a*c$ method, also called splitting the middle, or factoring by grouping.

Multiply $a$ times $c$ .

$5*-7=-35$

Find two numbers that when multiplied equal $-35$ , and when added equal the coefficient of the center term, $b=-2$ .

The numbers $5$ and $-7$ meet the criteria.

Rewrite the equation, replacing $-2x$ with the sum of $5x$ and $-7x$ .

$5x^2+5x-7x-7$

Group into two binomials.

$(5x^2+5x)-(7x-7)$ =

Factor out the GCF from each group.

$5x(x+1)-7(x+1)$

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

$(5x-7)(x+1)$

How do you factor completely: 5x^2 − 2x − 75x^2 − 2x − 7?