Factor 2a^2-7a+5

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

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

Factor $- 7$ out of $- 7 a$ .

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 a (a - 1) - 5 (a - 1)$

Step 3

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

$(a - 1) (2 a - 5)$

Factor 2a^2-7a+5

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