Factor 3x^2+22x-16

$3 x^{2} + 22 x - 16$

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 $a \cdot c = 3 \cdot - 16 = - 48$ and whose sum is $b = 22$ .

Factor $22$ out of $22 x$ .

$3 x^{2} + 22 (x) - 16$

Rewrite $22$ as $- 2$ plus $24$

$3 x^{2} + (- 2 + 24) x - 16$

Apply the distributive property.

$3 x^{2} - 2 x + 24 x - 16$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} - 2 x) + 24 x - 16$

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

$x (3 x - 2) + 8 (3 x - 2)$

Step 3

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

$(3 x - 2) (x + 8)$

Factor 3x^2+22x-16

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