General Strategy for Factoring Polynomials: example 7.65

Factor completely: $24 x^{3} + 81$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor completely: $250 m^{3} + 432$ .

How did it go?

Is there a GCF?	Yes, 3.	$24 x^{3} + 81$
Factor it out.		$3 (8 x^{3} + 27)$
In the parentheses, is it a binomial, trinomial, or are there more than three terms?	Binomial.
Is it a sum or difference?	Sum.
Of squares or cubes?	Sum of cubes.
Write it using the sum of cubes pattern.
Is the expression factored completely?	Yes.	$3 (2 x + 3) (4 x^{2} - 6 x + 9)$
Check by multiplying.		We leave the check to you.

Is there a GCF?	Yes, 3.	$24 x^{3} + 81$
Factor it out.		$3 (8 x^{3} + 27)$
In the parentheses, is it a binomial, trinomial, or are there more than three terms?	Binomial.
Is it a sum or difference?	Sum.
Of squares or cubes?	Sum of cubes.
Write it using the sum of cubes pattern.
Is the expression factored completely?	Yes.	$3 (2 x + 3) (4 x^{2} - 6 x + 9)$
Check by multiplying.		We leave the check to you.