Factor 84m^2-23m-42

$84 m^{2} - 23 m - 42$

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 $a \cdot c = 84 \cdot - 42 = - 3528$ and whose sum is $b = - 23$ .

Factor $- 23$ out of $- 23 m$ .

$84 m^{2} - 23 (m) - 42$

Rewrite $- 23$ as $49$ plus $- 72$

$84 m^{2} + (49 - 72) m - 42$

Apply the distributive property.

$84 m^{2} + 49 m - 72 m - 42$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(84 m^{2} + 49 m) - 72 m - 42$

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

$7 m (12 m + 7) - 6 (12 m + 7)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $12 m + 7$ .

$(12 m + 7) (7 m - 6)$

Factor 84m^2-23m-42

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