Factor 2c^2-23c+11

$2 c^{2} - 23 c + 11$

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 $a \cdot c = 2 \cdot 11 = 22$ and whose sum is $b = - 23$ .

Factor $- 23$ out of $- 23 c$ .

$2 c^{2} - 23 (c) + 11$

Rewrite $- 23$ as $- 1$ plus $- 22$

$2 c^{2} + (- 1 - 22) c + 11$

Apply the distributive property.

$2 c^{2} - 1 c - 22 c + 11$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 c^{2} - 1 c) - 22 c + 11$

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

$c (2 c - 1) - 11 (2 c - 1)$

Step 3

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

$(2 c - 1) (c - 11)$

Factor 2c^2-23c+11

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