Factor 5x^2-39x+28

$5 x^{2} - 39 x + 28$

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 $a \cdot c = 5 \cdot 28 = 140$ and whose sum is $b = - 39$ .

Factor $- 39$ out of $- 39 x$ .

$5 x^{2} - 39 (x) + 28$

Rewrite $- 39$ as $- 4$ plus $- 35$

$5 x^{2} + (- 4 - 35) x + 28$

Apply the distributive property.

$5 x^{2} - 4 x - 35 x + 28$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} - 4 x) - 35 x + 28$

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

$x (5 x - 4) - 7 (5 x - 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 4$ .

$(5 x - 4) (x - 7)$

Factor 5x^2-39x+28

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