Factor 2a^2-11a+5

$2 a^{2} - 11 a + 5$

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 $b = - 11$ .

Factor $- 11$ out of $- 11 a$ .

$2 a^{2} - 11 (a) + 5$

Rewrite $- 11$ as $- 1$ plus $- 10$

$2 a^{2} + (- 1 - 10) a + 5$

Apply the distributive property.

$2 a^{2} - 1 a - 10 a + 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 a^{2} - 1 a) - 10 a + 5$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 a - 1$ .

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

Factor 2a^2-11a+5

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