8/11 Algebra - Polynomial Unit Review

Give the y-intercept of y=-3x⁴-2x³+2x-1.

-1

Find the zeros and their multiplicities. y = -3(x+1)²(x-4)³

-1 (mult. of 2) 4 (mult. of 3)

Give the y-intercept of y=3x⁶-4x⁵+7x²-3.

-3

Find the zeros and their multiplicities. y = (x+3)²(x-1)³

-3 (mult. of 2) 1 (mult of 3)

Give the y-intercept of y=4x-3x³.

0

Find the zeros and their multiplicities. y = -3x(x+2)(x-5)

0 (mult of 1) -2 (mult of 1) 5 (mult of 1)

Find the zeros and their multiplicities. y = -2x(x-4)²

0 (mult of 1) 4 (mult of 2)

For a polynomial of degree 4, what would be the maximum number of real zeros and what would be the minimum number of real zeros possible?

The maximum would be 4 real zeros. The minimum would be 0 real zeros.

For a polynomial function of degree 5, what is the maximum number of real zeros and what is the minimum number of real zeros possible?

The maximum would be 5 real zeros. The minimum would be 1 real zero.

Approximate the real zero(s) to the nearest hundredth. y=3x³-2x²+1

x≈-.53

Approximate the real zero(s) to the nearest hundredth. y=-2x⁴+3x²+5

x≈-1.58 or x≈1.58

Approximate the real zero(s) to the nearest hundredth. y=x³+2x-1

x≈.45

Approximate the real zero(s) to the nearest hundredth. y=x⁴-2x+1

x≈.54 or x=1

Give the y-intercept of y=8x⁵-3x³+2.

2

Find the zeros and their multiplicities. y = (x-2)(x+5)(x+1)(x-4)

2 (mult of 1) -5 (mult of 1) -1 (mult of 1) 4 (mult of 1)

If 2+3i is a zero of a polynomial function, what other zero must exist for the function?

2-3i (from the Complex Conjugates Theorem)

Give the y-intercept of y=2x³-3x²+4x+3.

3

If -4i is a zero of a polynomial functions, what other zero must exist for the function?

4i (from the Complex Conjugates Theorem)