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Chapter 4: Q. 13 (page 245)

In Problems 13, find the remainder R when fxis divided by gx. Is ga factor of f?

f(x)=x4-2x3+15x-2;g(x)=x+2

Short Answer

Expert verified

The remainder R is 0.

Yes,gxis a factor offx

Step by step solution

01

Given information

f(x)=x4-2x3+15x-2;g(x)=x+2

02

Determine whether g is a factor of f

Note: When fxis divided by a linear polynomial gx, the remainder Ris equal to fcbased from the Remainder Theorem.

cis a real number from g(x)=x-c. In this problem, c=-2.

Substitute -2for xin fx.

f-2=-24-2-23+15-2-2=16+16-30-2=0

Since R=0,g(x) is a factor of fx.

03

Write the conclusion

The remainder is0.

Yes, gxis a factor offx.

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