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Chapter 7: Q. 306 (page 878)

In the following exercises, factor completely.

5n3+320

Short Answer

Expert verified

The factored form of the polynomial is5n+4n2-4n+16.

Step by step solution

01

Step 1. Given Information.

The given polynomial is 5n3+320.

02

Step 2. Factoring  

Let's find the GCF and factor out the GCF,

5n3+64

In the parentheses, the polynomial is a binomial and it is the type of the sum of cubes.

To factor, the given polynomial we will use the sum of cubes formula.

So,

5n3+64=5n3+43=5n+4n2-4n+42=5n+4n2-4n+16

The polynomial is factored completely.

Thus, the factored form is 5n+4n2-4n+16.

03

Step 3. Check the answer  

To check the answer, expand the factored form we get,

5n3+320=5n+4n2-4n+165n3+320=(5n+20)n2-4n+165n3+320=5n3-20n2+80n+20n2-80n+3205n3+320=5n3+320

L.H.S = R.H.S

Thus, the answer is right.

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