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Chapter 4: Q. 12 (page 245)

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

f(x)=8x3-3x2+x+4;g(x)=x-1

Short Answer

Expert verified

The remainder R is 10.

No,gxis not a factor offx

Step by step solution

01

Given information

The given function isf(x)=8x3-3x2+x+4;g(x)=x-1

02

Determine whether g is a factor of f

Note: When fxis divided by a linear polynomial gx, the remainder R is equal to f(c)based from the Remainder Theorem.

cis a real number from g(x)=x-c. In this problem, c=1.

Substitute 1for xin fx.

f(x)=813-312+1+4=8-3+1+4=10

Since,R=10,gxis not a factor offx

03

Write the conclusion

The remainder is 10.

No,gxis not a factor offx.

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Most popular questions from this chapter

Find the domain of the rational function.

G(x)=6x+34-x

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f(x)=4x4-15x3-8x2+15x+4

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