Factor 3x^2-16x+20

$3 x^{2} - 16 x + 20$

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 $a \cdot c = 3 \cdot 20 = 60$ and whose sum is $b = - 16$ .

Factor $- 16$ out of $- 16 x$ .

$3 x^{2} - 16 (x) + 20$

Rewrite $- 16$ as $- 6$ plus $- 10$

$3 x^{2} + (- 6 - 10) x + 20$

Apply the distributive property.

$3 x^{2} - 6 x - 10 x + 20$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} - 6 x) - 10 x + 20$

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

$3 x (x - 2) - 10 (x - 2)$

Step 3

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

$(x - 2) (3 x - 10)$

Factor 3x^2-16x+20

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