Factor 3c^2-10c+8

$3 c^{2} - 10 c + 8$

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 $a \cdot c = 3 \cdot 8 = 24$ and whose sum is $b = - 10$ .

Factor $- 10$ out of $- 10 c$ .

$3 c^{2} - 10 (c) + 8$

Rewrite $- 10$ as $- 4$ plus $- 6$

$3 c^{2} + (- 4 - 6) c + 8$

Apply the distributive property.

$3 c^{2} - 4 c - 6 c + 8$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 c^{2} - 4 c) - 6 c + 8$

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

$c (3 c - 4) - 2 (3 c - 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 c - 4$ .

$(3 c - 4) (c - 2)$

Factor 3c^2-10c+8

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