Factor 24m^2-32m+8

$24 m^{2} - 32 m + 8$

Step 1

Factor $8$ out of $24 m^{2} - 32 m + 8$ .

Factor $8$ out of $24 m^{2}$ .

$8 (3 m^{2}) - 32 m + 8$

Factor $8$ out of $- 32 m$ .

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

Factor $8$ out of $8$ .

$8 (3 m^{2}) + 8 (- 4 m) + 8 (1)$

Factor $8$ out of $8 (3 m^{2}) + 8 (- 4 m)$ .

$8 (3 m^{2} - 4 m) + 8 (1)$

Factor $8$ out of $8 (3 m^{2} - 4 m) + 8 (1)$ .

$8 (3 m^{2} - 4 m + 1)$

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 $a \cdot c = 3 \cdot 1 = 3$ and whose sum is $b = - 4$ .

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

$8 (3 m^{2} - 4 (m) + 1)$

Rewrite $- 4$ as $- 1$ plus $- 3$

$8 (3 m^{2} + (- 1 - 3) m + 1)$

Apply the distributive property.

$8 (3 m^{2} - 1 m - 3 m + 1)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$8 ((3 m^{2} - 1 m) - 3 m + 1)$

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

$8 (m (3 m - 1) - (3 m - 1))$

Factor the polynomial by factoring out the greatest common factor, $3 m - 1$ .

$8 ((3 m - 1) (m - 1))$

Remove unnecessary parentheses.

$8 (3 m - 1) (m - 1)$

Factor 24m^2-32m+8

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