Chapter 6Review

Write the polynomial in standard form.

−4x +2x3 −8x4

Write the polynomial in standard form.

−4x +2x3 −8x4

−8x4 +2x3 −4x

Write the polynomial in standard form.

(2x3 −4x2 +5x + 7) −(8x +2x3 −4x2 + 7)

Write the polynomial in standard form.

(2x3 −4x2 +5x + 7) −(8x +2x3 −4x2 + 7)

−3x

Name by degree and

by number of terms.

−4x +2x3 −8x2

Name by degree and

by number of terms.

• By degree – Cubic• By number of terms - Trinomial

−4x +2x3 −8x2

Name by degree and

by number of terms..

−2x4 + x2

Name by degree and

by number of terms..

• By degree – Quartic• By number of terms - Binomial

−2x4 + x2

Write the function in factored form.Determine the zeros and any multiplicity.

f (x) =x4 −3x3 −10x2

Write the function in factored form.Determine the zeros and any multiplicity.

f (x) =x4 −3x3 −10x2

The zeros are 0 (multiplicity 2), 5 and -2.

x2(x −5)(x +2)

Describe the end behavior of the function.

f (x) =x4 −3x3 −10x2

as f (x) → −∞, f (x) →  ___as f (x) →   ∞, f (x) → ___

Describe the end behavior of the function.

as f (x) → −∞, f (x) →  ∞as f (x) →   ∞, f (x) → ∞

f (x) =x4 −3x3 −10x2

Describe the end behavior of the function.

as f (x) → −∞, f (x) →  ___as f (x) →   ∞, f (x) → ___

f (x) =−2x3 +1

Describe the end behavior of the function.

f (x) =−2x3 +1

as f (x) → −∞, f (x) →   ∞as f (x) →   ∞, f (x) → −∞

Use the graph to approximate all relative minimums and maximums.

Use the graph to approximate all relative minimums and maximums.

Relative Maximum is 1.Relative Minimums are -7 and -1.5.

Divide using long division.

(6x3 +2x2 −11x +12) ÷(3x + 4)

Divide using long division.

2x2 −2x −1 R 16

(6x3 +2x2 −11x +12) ÷(3x + 4)

Divide using synthetic division.

(x3 −8x2 +17x −10) ÷(x −5)

Divide using synthetic division.

x2 −3x +2

(x3 −8x2 +17x −10) ÷(x −5)

Explain the error that was made in the following problem.

1 3 -1 2 -4 3 2 4 0 3 2 4 (3x4 −x3 +2x −4) ÷(x −1)

Explain the error that was made in the following problem.

The student forgot to insert a zero in the top line

for the term that is missing.

1 3 -1 2 -4 3 2 4 0 3 2 4 (3x4 −x3 +2x −4) ÷(x −1)

x2

List the possible rational zeros.Do not find the zeros.

f (x) =5x3 +2x2 −5x +15

List the possible rational zeros.Do not find the zeros.

f (x) =5x3 +2x2 −5x +15

±1, ±

1

5, ±3, ±

3

5, ±5, ±15

Given the roots of a polynomial to be -2 and -3i, you state the factors of the polynomial are (x+2) and (x+3i). Are you correct? Explain.

Given the roots of a polynomial to be -2 and -3i, you state the factors of the polynomial are (x+2)(x+3i). Are you correct? Explain. No, if -3i is a root, then 3i must also be a root

therefore the factors would be: (x+2)(x+3i)(x-3i)

Find all solutions (real and imaginary).

0 =8x3 −216

Find all solutions (real and imaginary).

0 =8x3 −216

x =3,

−3 ±3i 3

2

Find all solutions (real and imaginary).

−4 =x4 −5x2

Find all solutions (real and imaginary).

−4 =x4 −5x2

x =±1, ±2

Good Luck on the test.