Algebra Examples

$2 m^{6} - 24 m^{5} + 64 m^{4}$

Step 1

Factor out the GCF of $2 m^{4}$ from $2 m^{6} - 24 m^{5} + 64 m^{4}$ .

Tap for more steps...

Step 1.1

Factor out the GCF of $2 m^{4}$ from each term in the polynomial.

Tap for more steps...

Step 1.1.1

Factor out the GCF of $2 m^{4}$ from the expression $2 m^{6}$ .

$2 m^{4} (m^{2}) - 24 m^{5} + 64 m^{4}$

Step 1.1.2

Factor out the GCF of $2 m^{4}$ from the expression $- 24 m^{5}$ .

$2 m^{4} (m^{2}) + 2 m^{4} (- 12 m) + 64 m^{4}$

Step 1.1.3

Factor out the GCF of $2 m^{4}$ from the expression $64 m^{4}$ .

$2 m^{4} (m^{2}) + 2 m^{4} (- 12 m) + 2 m^{4} (32)$

Step 1.2

Since all the terms share a common factor of $2 m^{4}$ , it can be factored out of each term.

$2 m^{4} (m^{2} - 12 m + 32)$

Step 2

Factor $m^{2} - 12 m + 32$ using the AC method.

Tap for more steps...

Step 2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $32$ and whose sum is $- 12$ .

$- 8, - 4$

Step 2.2

Write the factored form using these integers.

$2 m^{4} ((m - 8) (m - 4))$