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Chapter 7: Q. 298 (page 878)

In the following exercises, factor completely.

5t3-40

Short Answer

Expert verified

The factored form of the polynomial is5t3-40=5(t-2)(t2+2t+4).

Step by step solution

01

Step 1. Given Information.  

The given Polynomial is5t3-40.

02

Step 2. Factoring by the formula for the difference of cubes. 

Terms of a polynomial have a common factor5.

5t3-40=5(t3-8)

In the parentheses, it is a binomial of the difference of cubes.

Factorize it by using the formula for the difference of cubes.

5t3-40=5(t3-8)5t3-40=5(t3-23)5t3-40=5(t-2)(t2+2t+22)5t3-40=5(t-2)(t2+2t+4)

Polynomial cannot be factored further.

So factored form islocalid="1647946607143" role="math" 5t3-40=5(t-2)(t2+2t+4).

03

Step 3. Verification.  

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

5t3-40=5(t-2)(t2+2t+4)5t3-40=5t(t2+2t+4)-2(t2+2t+4)5t3-40=5t3+2t2+4t-2t2-4t-85t3-40=5t3-85t3-40=5t3-40

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

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