Factor 3s^2-8s+5

$3 s^{2} - 8 s + 5$

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 $a \cdot c = 3 \cdot 5 = 15$ and whose sum is $b = - 8$ .

Factor $- 8$ out of $- 8 s$ .

$3 s^{2} - 8 (s) + 5$

Rewrite $- 8$ as $- 3$ plus $- 5$

$3 s^{2} + (- 3 - 5) s + 5$

Apply the distributive property.

$3 s^{2} - 3 s - 5 s + 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 s^{2} - 3 s) - 5 s + 5$

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

$3 s (s - 1) - 5 (s - 1)$

Step 3

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

$(s - 1) (3 s - 5)$

Factor 3s^2-8s+5

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