Question

Explain, in complete sentences, how you would factor

8x^6 – 56x^3 + 98.

Answer 1

\[8x^6 – 56x^3 + 98.\]

Answer 2

You would add your like terms, in this case you want to factor 8x^6 and 56x^2, after you factor that you will want to incorporate your 98 into the factor.

Answer 3

i understand first part but the "after that" i dont get

Answer 4

Find the LCD for all your terms:
In this case they all have 2 in common.

8x⁶ - 56x³ + 98

Factor out 2

2(4x⁶ - 28x³ + 49) <=== Just divided it by 2 and put a 2 on the outside to show that if we multiply these terms by 2 we will get the same outcome.

4x⁶ - 28x³ + 49 can be factored further. Notice it is a Perfect Square Trinomial.

2(2x^3 - 7)(2x^3 - 7) <=== Now you will create two sets of binomials:

You see that the terms in parenthesis are both the same, thus we can simply further and say: 2(2x³ - 7)²