Synthetic Division and the Remainder Theorem

Question 1

Complete the steps to identify all potential rational roots of f(x) = 3x2 – x – 4.Values of p are factors of .

Revolt · Accepted Answer

-4

Question 2

Values of q are factors of .

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3

Question 3

Check all of the numbers that are potential rational roots of f(x) = x4 – 2x3 + 5x2 – 7x + 9.

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±1; ±3; ±9

Question 4

The graph of f(x) = 2x3 +x2 – 4x – 2 is shown.How many of the roots of f(x) are rational?

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1

Question 5

of the polynomial.

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definitely a root

Question 6

Complete the steps to solve the polynomial equation x3 – 21x = –20.According to the rational root theorem, which number is a potential root of the polynomial?

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1

Question 7

Complete the statement with the choice that best describes the relationship between the polynomial and its rational zeroes.A polynomial, P, has a leading coefficient of 1 and a constant term. The rational roots of P are all .

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factors of the constant term

Question 8

If x = 1 2 , then x − 1 2 = 0. This is the same as = 0.

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2x – 1

Question 9

Use the synthetic division shown to help factor the polynomial and solve the equation. What are the solutions of the equation?

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1, 4, and –5

Question 10

In completely factored form, f(x) = .

Revolt · Accepted Answer

(x + 1)(x – 2)(2x – 1)²

Synthetic Division and the Remainder Theorem Answers

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