Chapter 4: Q. 92 (page 210)

Use the Factor Theorem to prove that $x + c$ is a factor of
role="math" localid="1646067091231" $x^{n} + c^{n}$ if $n \geq 1$ is an odd integer

Short Answer

Expert verified

If $f (x) = x^{n} + c^{n}$ and n is a positive odd integer then $f (- c) = 0$ so $x + c$ is a factor of $x^{n} + c^{n}$ whenn is a positive odd integer

Step by step solution

Step 1. given data

The given expression is

$x^{n} + c^{n}$

Factor is $x + c$

Step 2. proof

Consider function $f (x) = x^{n} + c^{n}$

According to Factor Theorem, If $x + c$ is a factor of function then $f (- c) = 0$

substitute c for x in the function

$f (x) = x^{n} + c^{n} f (- c) = {(- c)}^{n} + c^{n}$

n is a positive odd integer

localid="1646067391807" $f (- c) = - c^{n} + c^{n} f (- c) = 0$

the function value is zero for $x = - c$

so $x + c$ is a factor of $x^{n} + c^{n}$ when $n \geq 1$

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Use the Factor Theorem to prove that $x + c$ is a factor of
role="math" localid="1646067091231" $x^{n} + c^{n}$ if $n \geq 1$ is an odd integer

Short Answer

Step by step solution

Step 1. given data

Step 2. proof

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Use the Factor Theorem to prove that x+c is a factor ofrole="math" localid="1646067091231" xn+cn if n≥1 is an odd integer

Short Answer

Step by step solution

Step 1. given data

Step 2. proof

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Use the Factor Theorem to prove that $x + c$ is a factor of
role="math" localid="1646067091231" $x^{n} + c^{n}$ if $n \geq 1$ is an odd integer