Factor 5a^2-4a-28

$5 a^{2} - 4 a - 28$

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 $a \cdot c = 5 \cdot - 28 = - 140$ and whose sum is $b = - 4$ .

Factor $- 4$ out of $- 4 a$ .

$5 a^{2} - 4 (a) - 28$

Rewrite $- 4$ as $10$ plus $- 14$

$5 a^{2} + (10 - 14) a - 28$

Apply the distributive property.

$5 a^{2} + 10 a - 14 a - 28$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 a^{2} + 10 a) - 14 a - 28$

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

$5 a (a + 2) - 14 (a + 2)$

Step 3

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

$(a + 2) (5 a - 14)$

Factor 5a^2-4a-28

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