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Chapter 7: Q. 279 (page 878)

In the following exercises, factor completely.

10x4+35x3

Short Answer

Expert verified

The factored form of the polynomial is10x4+35x=5x3(2x+7).

Step by step solution

01

Step 1. Given Information.

The Given Polynomial is10x4+35x3.

02

Step 2. Factoring by greatest common factor method.

Terms of a polynomial have the common factor of5x3.

so factor out the greatest common factor in the polynomial.

10x4+35x3=5x3(2x)+(7)5x3=5x3(2x+7)

In the parentheses, it is a binomial of the sum of terms, that cannot be factored.

So factored form is10x4+35x=5x3(2x+7).

03

Step 3. Verification.

Check whether the expanded form of the factored polynomial is equal to the original polynomial or not.

10x4+35x=?5x3(2x+7)10x4+35x=?5x3(2x)+5x3(7)10x4+35x=10x4+35x

The left-hand side is equal to the right-hand side so factored form is correct.

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