Multiplicity and Possible Real Roots of Polynomials

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

• -2, 7 multiplicity 3

• -2, 7, 3

• 2, -7 multiplicity 3

• 2, -7, 3

Which statement is correct?

• The zeros of this polynomial are 0, 2, and 5. 

• The solution 5 has a multiplicity of 2

• The solution 1 has a multiplicity of 1

• There are 4 solutions. 

A graph of a polynomial equation of degree 5 has three real x-intercepts (touches the x- intercept at 3 different points). Check off ALL the possible situations of what type of roots they could be.

• Double Root, Double Root, Triple Root

• Single Root, Double Root, Double Root

• Single Root, Single Root, Single Root, Two Imaginaries

• Single Root, Single Root, Double Root, Imaginary

• Single Root, Triple Root, Single Root

Find the zeroes of the function. State the multiplicity of each zero.

• -7 with multiplicity 2; 3 with multiplicity 4

• -7 with multiplicity 1; 3 with multiplicity 1

• 7 with multiplicity 2; -3 with multiplicity 4

• 7 with multiplicity 1; -3 with multiplicity 1

• 7

• 2

• 6

• 4

Find the zeros of the polynomial f(x) = 2x³ + 5x² - 3x

• x = 0, 1/2, 3

• x = 1/2, -3

• x= 0, 1/2 , - 3

• x = 0, -1/2, 3

Find the zeros: y = x(x - 1)(x + 3)

• 0, 1, -3

• -3, 1

• -1, 3, 0

• -1, 3

We Do:

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

• -3

• -4

• 1

• 6

State the x-intercepts of:

y = -3(x - 4)(x + 6)

• (12, 0) and (-18, 0)

• (-12, 0) and (-6, 0)

• (-4, 0) and (6, 0)

• (4, 0) and (-6, 0)

Determine the linear factors of the polynomial function whose zeros are 0, -1, and -3.

Mathematical Equivalence

ON