Lesson 10

Multiplicity

The practice problem answers are available at one of our IM Certified Partners

Problem 1

Draw a rough sketch of the graph of \(g(x)=(x-3)(x+1)(7x-2)\).

Problem 2

Draw a rough sketch of the graph of \(f(x)=(x+1)^2(x-4)\).

Problem 3

Technology required. Predict the end behavior of each polynomial function, then check your prediction using technology.

  1. \(A(x) = (x + 3)(x - 4)(3x - 7)(4x - 3)\)
  2. \(B(x) = (3 - x)^2(6 - x)\)
  3. \(C(x) = \text-(4 - 3x)(x^4)\)
  4. \(D(x) = (6 - x)^6\)

Problem 4

Which term can be added to the polynomial expression \(5x^{7}-6x^{6}+4x^4-4x^2\) to make it into a 10th degree polynomial?​​

A:

10

B:

$5x^3$

C:

$5x^7$

D:

$x^{10}$

(From Algebra2, Unit 2, Lesson 3.)

Problem 5

\(f(x)=(x+1)(x-6)\) and \(g(x)=2(x+1)(x-6)\). The graphs of each are shown.

Coordinate plane, x, negative 5 to 9 by 1, y, negative 25 to 10 by 5. Parabola, solid, through negative 1 comma 0 & 6 comma 0, minimum at 2 point 5 comma negative 12 point 2 5. Dotted parabola, same x-intercepts, minimum at 2 point 5 comma negative 24 point 5.
  1. Which graph represents which polynomial function? Explain how you know.
(From Algebra2, Unit 2, Lesson 6.)

Problem 6

State the degree and end behavior of \(f(x)=8x^3+2x^4-5x^2+9\). Explain or show your reasoning.

(From Algebra2, Unit 2, Lesson 8.)

Problem 7

The graph of a polynomial function \(f\) is shown. Select all the true statements about the polynomial.

polynomial function graphed. x intercepts = about -2 point 6 and 2 point 6. y intercept = 3. f of f decreases as x increases. 
A:

The degree of the polynomial is even.

B:

The degree of the polynomial is odd.

C:

The leading coefficient is positive.

D:

The leading coefficient is negative.

E:

The constant term of the polynomial is positive.

F:

The constant term of the polynomial is negative.

(From Algebra2, Unit 2, Lesson 9.)