Factor by Grouping 8m^2-2m-3

$8 m^{2} - 2 m - 3$

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 $a \cdot c = 8 \cdot - 3 = - 24$ and whose sum is $b = - 2$ .

Factor $- 2$ out of $- 2 m$ .

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

Rewrite $- 2$ as $4$ plus $- 6$

$8 m^{2} + (4 - 6) m - 3$

Apply the distributive property.

$8 m^{2} + 4 m - 6 m - 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 m^{2} + 4 m) - 6 m - 3$

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

$4 m (2 m + 1) - 3 (2 m + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 m + 1$ .

$(2 m + 1) (4 m - 3)$

Factor by Grouping 8m^2-2m-3

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