Factor by Grouping 8m^2-18m-5

$8 m^{2} - 18 m - 5$

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 $a \cdot c = 8 \cdot - 5 = - 40$ and whose sum is $b = - 18$ .

Factor $- 18$ out of $- 18 m$ .

$8 m^{2} - 18 (m) - 5$

Rewrite $- 18$ as $2$ plus $- 20$

$8 m^{2} + (2 - 20) m - 5$

Apply the distributive property.

$8 m^{2} + 2 m - 20 m - 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 m^{2} + 2 m) - 20 m - 5$

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

$2 m (4 m + 1) - 5 (4 m + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 m + 1$ .

$(4 m + 1) (2 m - 5)$

Factor by Grouping 8m^2-18m-5

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