Factor 5x^2-13x+8

$5 x^{2} - 13 x + 8$

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 $a \cdot c = 5 \cdot 8 = 40$ and whose sum is $b = - 13$ .

Factor $- 13$ out of $- 13 x$ .

$5 x^{2} - 13 (x) + 8$

Rewrite $- 13$ as $- 5$ plus $- 8$

$5 x^{2} + (- 5 - 8) x + 8$

Apply the distributive property.

$5 x^{2} - 5 x - 8 x + 8$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} - 5 x) - 8 x + 8$

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

$5 x (x - 1) - 8 (x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

$(x - 1) (5 x - 8)$

Factor 5x^2-13x+8

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