Factor 5x^2-7x+2

$5 x^{2} - 7 x + 2$

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 $a \cdot c = 5 \cdot 2 = 10$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

$5 x^{2} - 7 (x) + 2$

Rewrite $- 7$ as $- 2$ plus $- 5$

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$x (5 x - 2) - (5 x - 2)$

Step 3

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

$(5 x - 2) (x - 1)$

Factor 5x^2-7x+2

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