Factor 5x^2-33x-14

$5 x^{2} - 33 x - 14$

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 $a \cdot c = 5 \cdot - 14 = - 70$ and whose sum is $b = - 33$ .

Factor $- 33$ out of $- 33 x$ .

$5 x^{2} - 33 (x) - 14$

Rewrite $- 33$ as $2$ plus $- 35$

$5 x^{2} + (2 - 35) x - 14$

Apply the distributive property.

$5 x^{2} + 2 x - 35 x - 14$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + 2 x) - 35 x - 14$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 2$ .

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

Factor 5x^2-33x-14

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