Factor 15r^2+141r-90

$15 r^{2} + 141 r - 90$

Step 1

Factor $3$ out of $15 r^{2} + 141 r - 90$ .

Factor $3$ out of $15 r^{2}$ .

$3 (5 r^{2}) + 141 r - 90$

Factor $3$ out of $141 r$ .

$3 (5 r^{2}) + 3 (47 r) - 90$

Factor $3$ out of $- 90$ .

$3 (5 r^{2}) + 3 (47 r) + 3 (- 30)$

Factor $3$ out of $3 (5 r^{2}) + 3 (47 r)$ .

$3 (5 r^{2} + 47 r) + 3 (- 30)$

Factor $3$ out of $3 (5 r^{2} + 47 r) + 3 (- 30)$ .

$3 (5 r^{2} + 47 r - 30)$

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 $a \cdot c = 5 \cdot - 30 = - 150$ and whose sum is $b = 47$ .

Factor $47$ out of $47 r$ .

$3 (5 r^{2} + 47 (r) - 30)$

Rewrite $47$ as $- 3$ plus $50$

$3 (5 r^{2} + (- 3 + 50) r - 30)$

Apply the distributive property.

$3 (5 r^{2} - 3 r + 50 r - 30)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((5 r^{2} - 3 r) + 50 r - 30)$

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

$3 (r (5 r - 3) + 10 (5 r - 3))$

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

$3 ((5 r - 3) (r + 10))$

Remove unnecessary parentheses.

$3 (5 r - 3) (r + 10)$

Factor 15r^2+141r-90

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