Factor 5x^2+2x-3

$5 x^{2} + 2 x - 3$

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 $a \cdot c = 5 \cdot - 3 = - 15$ and whose sum is $b = 2$ .

Factor $2$ out of $2 x$ .

$5 x^{2} + 2 (x) - 3$

Rewrite $2$ as $- 3$ plus $5$

$5 x^{2} + (- 3 + 5) x - 3$

Apply the distributive property.

$5 x^{2} - 3 x + 5 x - 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} - 3 x) + 5 x - 3$

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

$x (5 x - 3) + 1 (5 x - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 3$ .

$(5 x - 3) (x + 1)$

Factor 5x^2+2x-3

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