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Chapter 4: Q. 10 (page 209)

True or False If fis a polynomial function of degree 4and if f(2)=5, then

role="math" localid="1646217783867" f(x)x-2=p(x)+5x-2

where p(x) is a polynomial function of degree 3.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Step 1. GIven information.

The given statement is,

If fis a polynomial function of degree 4and if f(2)=5, then

f(x)x-2=p(x)+5x-2

where p(x)is a polynomial function of degree 3.

02

Step 2. Explanation.

We know that if fis a polynomial divided by x-cthen the degree of the quotient polynomial is one less than that of the polynomial f.

Here the degree of polynomial fis 4and divided by x-2then the degree of the quotient p(x)will be 3.

Therefore, the given statement is true.

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Most popular questions from this chapter

Use the Factor Theorem to prove that x+c is a factor of

role="math" localid="1646067091231" xn+cn if n鈮�1 is an odd integer

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asymptote.

In Problems 7-44, follow Steps 1through 7 on page 228to analyze the graph of each function.

G(x)=x3+1x2+2x

Analyze each polynomial function using Steps 1through 8:

f(x)=x4-x3-6x2+4x+8.

Graph each rational function using transformations.

R(x)=x-4x
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