Factor 3s^2-14s+8

$3 s^{2} - 14 s + 8$

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 $b = - 14$ .

Factor $- 14$ out of $- 14 s$ .

$3 s^{2} - 14 (s) + 8$

Rewrite $- 14$ as $- 2$ plus $- 12$

$3 s^{2} + (- 2 - 12) s + 8$

Apply the distributive property.

$3 s^{2} - 2 s - 12 s + 8$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 s^{2} - 2 s) - 12 s + 8$

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

$s (3 s - 2) - 4 (3 s - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 s - 2$ .

$(3 s - 2) (s - 4)$

Factor 3s^2-14s+8

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