Factor 8m^2-44m+48

$8 m^{2} - 44 m + 48$

Step 1

Factor $4$ out of $8 m^{2} - 44 m + 48$ .

Factor $4$ out of $8 m^{2}$ .

$4 (2 m^{2}) - 44 m + 48$

Factor $4$ out of $- 44 m$ .

$4 (2 m^{2}) + 4 (- 11 m) + 48$

Factor $4$ out of $48$ .

$4 (2 m^{2}) + 4 (- 11 m) + 4 (12)$

Factor $4$ out of $4 (2 m^{2}) + 4 (- 11 m)$ .

$4 (2 m^{2} - 11 m) + 4 (12)$

Factor $4$ out of $4 (2 m^{2} - 11 m) + 4 (12)$ .

$4 (2 m^{2} - 11 m + 12)$

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 $a \cdot c = 2 \cdot 12 = 24$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 m$ .

$4 (2 m^{2} - 11 (m) + 12)$

Rewrite $- 11$ as $- 3$ plus $- 8$

$4 (2 m^{2} + (- 3 - 8) m + 12)$

Apply the distributive property.

$4 (2 m^{2} - 3 m - 8 m + 12)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$4 ((2 m^{2} - 3 m) - 8 m + 12)$

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

$4 (m (2 m - 3) - 4 (2 m - 3))$

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

$4 ((2 m - 3) (m - 4))$

Remove unnecessary parentheses.

$4 (2 m - 3) (m - 4)$

Factor 8m^2-44m+48

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