Factor 4n^2+62n-32

$4 n^{2} + 62 n - 32$

Step 1

Factor $2$ out of $4 n^{2} + 62 n - 32$ .

Factor $2$ out of $4 n^{2}$ .

$2 (2 n^{2}) + 62 n - 32$

Factor $2$ out of $62 n$ .

$2 (2 n^{2}) + 2 (31 n) - 32$

Factor $2$ out of $- 32$ .

$2 (2 n^{2}) + 2 (31 n) + 2 (- 16)$

Factor $2$ out of $2 (2 n^{2}) + 2 (31 n)$ .

$2 (2 n^{2} + 31 n) + 2 (- 16)$

Factor $2$ out of $2 (2 n^{2} + 31 n) + 2 (- 16)$ .

$2 (2 n^{2} + 31 n - 16)$

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 2 \cdot - 16 = - 32$ and whose sum is $b = 31$ .

Factor $31$ out of $31 n$ .

$2 (2 n^{2} + 31 (n) - 16)$

Rewrite $31$ as $- 1$ plus $32$

$2 (2 n^{2} + (- 1 + 32) n - 16)$

Apply the distributive property.

$2 (2 n^{2} - 1 n + 32 n - 16)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((2 n^{2} - 1 n) + 32 n - 16)$

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

$2 (n (2 n - 1) + 16 (2 n - 1))$

Factor the polynomial by factoring out the greatest common factor, $2 n - 1$ .

$2 ((2 n - 1) (n + 16))$

Remove unnecessary parentheses.

$2 (2 n - 1) (n + 16)$

Factor 4n^2+62n-32

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