Factor by Grouping 63n^3+54n^2-105n-90

$63 n^{3} + 54 n^{2} - 105 n - 90$

Step 1

Factor out the GCF of $3$ from $63 n^{3} + 54 n^{2} - 105 n - 90$ .

Factor out the GCF of $3$ from each term in the polynomial.

Factor out the GCF of $3$ from the expression $63 n^{3}$ .

$3 (21 n^{3}) + 54 n^{2} - 105 n - 90$

Factor out the GCF of $3$ from the expression $54 n^{2}$ .

$3 (21 n^{3}) + 3 (18 n^{2}) - 105 n - 90$

Factor out the GCF of $3$ from the expression $- 105 n$ .

$3 (21 n^{3}) + 3 (18 n^{2}) + 3 (- 35 n) - 90$

Factor out the GCF of $3$ from the expression $- 90$ .

$3 (21 n^{3}) + 3 (18 n^{2}) + 3 (- 35 n) + 3 (- 30)$

Since all the terms share a common factor of $3$ , it can be factored out of each term.

$3 (21 n^{3} + 18 n^{2} - 35 n - 30)$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 ((21 n^{3} + 18 n^{2}) - 35 n - 30)$

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

$3 (3 n^{2} (7 n + 6) - 5 (7 n + 6))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 n + 6$ .

$3 ((7 n + 6) (3 n^{2} - 5))$