Question

Match the steps to factor a polynomial with four terms by grouping. Use grouping to factor 20a4 - 10a3 + 12a2 - 6a.

Answer 1

2a(2a - 1)(5a^2 + 3)

Explanation:

You can start by grouping the terms into two groups:

20a^4 - 10a^3 and 12a^2 - 6a

Next, you can factor them:

(20a^4 - 10a^3) + (12a^2 - 6a)

10a^3(2a - 1) + 6a(2a -1)

Now, you can factor out the expression 2a - 1 to get:

(2a - 1)(10a^3 + 6a)

In the second factor, the two terms have a GCF of 2a, so you can factor that out:

2a(2a - 1)(5a^2 + 3)

Answer 2

Explanation:

The first two factor as

10a^3 ( 2a - 1)

The second two factor as

6a (2a - 1)

When you put them together, the common factor is 2a - 1

(10a^3 - 6a) (2a - 1) Can you factor any further? Yes. Try taking out 2a out of the first factor

2a(5a^2 - 3) Now what you have is

2a(5a^2 - 3)(2a - 1) Don't go any further.