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Chapter 5: Q.334. (page 552)

Use the factor theorem to determine whetherx+3a factor ofx3+8x2+21x+18.

Short Answer

Expert verified

Yes,x+3is a factor ofx3+8x2+21x+18.

Step by step solution

01

Step 1. Given information.

fx=x3+8x2+21x+18and x+3 is the factor of polynomial function.

02

Step 2. To simplify the polynomial function, by using the remainder theorem.

According to the remainder theorem, x+3is a factor of fx=x3+8x2+21x+18if f-3=0.

Substitute x=-3in fx=x3+8x2+21x+18.

f-3=-33+8-32+21-3+18鈬�-27+8路9-63+18鈬�-27+72-63+18鈬�90-90鈬�0

03

Step 3. Simplified answer.

Since f-3=0.

Hence,x+3is a factor offx=x3+8x2+21x+18.

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