Algebra 2 Rational Root Theorem, Remainder Theorem, Factor Theorem, Descartes Rule of Signs and Fundamental Theorem of A

What are the zeros (x-intercepts)?

• x = 4, 7

• x = -1, 4/7

• x = -4/7, 1

• x = 7, -4

Find the zeros of polynomial given one zero.

• A

• B

• C

• D

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

How many possible negatives solutions does the following polynomial have? f(x) = x⁴ - 3x³ - 17x² + 39x -20

• 3 or 1

• 3

• 1

• 2 or 0

How many positive solutions does the following polynomial have? f(x) =3x⁵ - x⁴ + 3x² - 6x +11

• 4, 2, or 0

• 4

• 3 or 1

• 3

How many possible positive solutions does the following polynomial have?

f(x) =3x⁵ - x⁴ + 3x² - 6x +11

• 3

• 4 or 2

• 3 or 1

• 4, 2, or 0

Which of these is a possible rational root of the polynomials? x³ - 6x² - x + 30

• 0

• 4

• -9

• -15

Use Descartes Rule of Signs to determine the possible number of positive and negative real roots.

• 2 positive, 0 negative

• 1 positive, 1 negative

• 0 positive, 2 negative

• 0 positive, 0 negative

Use Descartes Rule of Signs to determine the possible number of positive and negative real roots.

• 3 or 1 positive roots and 0 negative roots

• 4, 2, or 0 positive roots and 1 negative root

• 4, 2, or 0 positive roots and 0 negative roots

• 2 or 0 positive roots and 1 negative roots

Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

• ±1, ±8

• ±1, ±2, ±4, ±8

• ±1, ±2, ±4

• 1, 2, 4, 8