Factor m-6+15m^2

$m - 6 + 15 m^{2}$

Step 1

Reorder terms.

$15 m^{2} + m - 6$

Step 2

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 $a \cdot c = 15 \cdot - 6 = - 90$ and whose sum is $b = 1$ .

Multiply by $1$ .

$15 m^{2} + 1 m - 6$

Rewrite $1$ as $- 9$ plus $10$

$15 m^{2} + (- 9 + 10) m - 6$

Apply the distributive property.

$15 m^{2} - 9 m + 10 m - 6$

Step 3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 m^{2} - 9 m) + 10 m - 6$

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

$3 m (5 m - 3) + 2 (5 m - 3)$

Step 4

Factor the polynomial by factoring out the greatest common factor, $5 m - 3$ .

$(5 m - 3) (3 m + 2)$

Factor m-6+15m^2

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