Algebra II 6-5 through 6-8 Practice Quiz

Find all the real zeros of the function

f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

Find possible rational zeros and plug in for x to find which equals 0 or use synthetic division to see which answers have a remainder of 0.

• x = 1/2, -6

• x = -1/2, 6

• x = 4, -1/2, 6

• x = -4, 1/2, -6

Find the roots of 0=x³-4x²+2x-8

Use synthetic division with the real zero, and then use quadratic formula.

• ±2,4

• ±2i,4

• ±i√2,4

• ±√2,4

What are the possible rational roots for the polynomial

x³+ 10x²- 35x + 22

Lesson 6.5 (p/q)

• 1, 2, 11, 22

• 1, -1, 2, -2

• 1, -1, 2, -2, 11, -11, 22, -22

• 1, 2

List the potential real zeros of:

f(x) = 5x³ - x² + 3

Lesson 6.5 (p/q)

• ±1/5, ±3/5, ±1, ±3

• ±1/3, ±5/3, ±1, ±5

• ±1/5, ±3/5, ±1, ±3, ±5

• ±1/5, ±1/3, ±1, ±3, ±5

The polynomial

f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

In other words, what is the degree?

• 5

• 4

• 3

• 2

What are the roots of the polynomial function?

y = (x + 2)(x - 7)³

^{Set the factors equal to 0 to solve for x. The multiplicity is the degree of the factor.}

• -2, 7 multiplicity 3

• -2, 7, 3

• 2, -7 multiplicity 3

• 2, -7, 3

State the zeros of the polynomial (include multiplicity):

f(x) = x(x+3)²(x - 2)

Set the factors equal to 0 to solve for x. The multiplicity is the degree of the factor.

• x = 0, 3, 2

• x = 0, -3 (multiplicity of 2), 2

• -3, 2

• 0, 2 (multiplicity of 3)

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.

Identify the degree of the polynomial and the sign of the leading coefficient.

Positive leading coefficient, right side of graph is up

Negative leading coefficient, right side of the graph is down

Even degree, same direction

Odd degree, opposite directions

• Leading Coefficient Positive

  Degree - Even

• Leading Coefficient Positive

  Degree - Odd

• Leading Coefficient Negative

  Degree - Even

• Leading Coefficient Negative

  Degree - Odd

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.

Identify the degree of the polynomial and the sign of the leading coefficient.

Positive leading coefficient, right side of graph is up

Negative leading coefficient, right side of the graph is down

Even degree, same direction

Odd degree, opposite directions

• Leading Coefficient Positive

  Degree - Even

• Leading Coefficient Positive

  Degree - Odd

• Leading Coefficient Negative

  Degree - Even

• Leading Coefficient Negative

  Degree - Odd

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.

Identify the degree of the polynomial and the sign of the leading coefficient.

Positive leading coefficient, right side of graph is up

Negative leading coefficient, right side of the graph is down

Even degree, same direction

Odd degree, opposite directions

• Leading Coefficient Positive

  Degree - Even

• Leading Coefficient Positive

  Degree - Odd

• Leading Coefficient Negative

  Degree - Even

• Leading Coefficient Negative

  Degree - Odd