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Chapter 5: Q. 509 (page 564)

Use the Factor Theorem to determine if x+3is a factor of x3+8x2+21x+18.

Short Answer

Expert verified

x+3 is a factor of the given polynomial.

Step by step solution

01

Step 1. Given information 

  • The given polynomial is x3+8x2+21x+18.
  • The given factor isx+3.
02

Step 2. Applying Factor Theorem

  • By factor theorem, if x+3is a factor, then the value of the polynomial at x=-3will be 0.
  • Find the value of the polynomial at x=-3.

-33+8-32+21-3+18=-27+72-63+18=0

  • So,x+3is a factor of the polynomialx3+8x2+21x+18.

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