Factor 4x^2-3x-7

$4 x^{2} - 3 x - 7$

Step 1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot - 7 = - 28$ and whose sum is $b = - 3$ .

Factor $- 3$ out of $- 3 x$ .

$4 x^{2} - 3 (x) - 7$

Rewrite $- 3$ as $4$ plus $- 7$

$4 x^{2} + (4 - 7) x - 7$

Apply the distributive property.

$4 x^{2} + 4 x - 7 x - 7$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} + 4 x) - 7 x - 7$

Factor out the greatest common factor (GCF) from each group.

$4 x (x + 1) - 7 (x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x + 1$ .

$(x + 1) (4 x - 7)$

Factor 4x^2-3x-7

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