Synthetic Division and the Remainder Theorem Answers

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

Values of q are factors of .

Select all of the potential roots.

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

f(x) = 4x4 – 8x3 – 3x2 +7x – 2 = (x + 1)(4x3 – 12x2 +9x – 2)Look at the graph. Which of the following potential roots should you test next?

of the polynomial.

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?

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 .

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

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

In completely factored form, f(x) = .

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

Which of the values shown are potential roots of f(x) = 3x3 – 13x2 – 3x + 45? Select all that apply.