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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