Factor 7x^2-45x-28

$7 x^{2} - 45 x - 28$

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 $a \cdot c = 7 \cdot - 28 = - 196$ and whose sum is $b = - 45$ .

Factor $- 45$ out of $- 45 x$ .

$7 x^{2} - 45 (x) - 28$

Rewrite $- 45$ as $4$ plus $- 49$

$7 x^{2} + (4 - 49) x - 28$

Apply the distributive property.

$7 x^{2} + 4 x - 49 x - 28$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} + 4 x) - 49 x - 28$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x + 4$ .

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

Factor 7x^2-45x-28

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