Algebra 2: Rational Zero Theorem and Remainder Theorem and Fundamental Theorem of Algebra

What are the zeros of the graph?

• -4, -1, 2, 1 multiplicity 2

• -4, -1, 1, 2

• 4, 1, -2, -1 multiplicity 2

• 4, 1, -1, -2

How many zeroes are shown in the graph?

• 1

• 2

• 3

• 4

List all the possible rational zeros
h(x) = x³ - 5x²+2x+12

• 1,2,3,4,6,12

• 1,2,6,12

• 1,2,3,4,6,12,-1,-2,-3,-4,-6,-12

List all of the possible rational zeros

p(x) = 3x²+x+7

• -1/3, -7/3, -1, -7, 1/3, 7/3, 1, 7

• 1/3, 7/3, 1, 7

• 1, 7, 14, 21

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

• -3

• -4

• 1

• 6

What are the zeros (x-intercepts)?

• x = 4, 7

• x = -1, 4/7

• x = -4/7, 1

• x = 7, -4

Is (x-2) a factor of             f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.

• No, (x-2) is  not a factor. The remainder is zero.

• Yes, (x-2) is a factor. The remainder is zero.

• No, (x-2) is  not a factor. There is a remainder. 

Find the zeros of polynomial given one zero.

• A

• B

• C

• D

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

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

• positive, 2 or 0 negative

• positive, 1 negative

• 0 positive, 1 negative

• positive, 0 negative