Solving Higher Order Polynomial Equations

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

• 5

• 4

• 3

• 2

What is the relationship between the degree of a polynomial and the number of roots?

• The degree of a polynomial is inversely proportional to the number of roots

• The degree of a polynomial determines the maximum number of roots the polynomial can have.

• The degree of a polynomial determines the minimum number of roots the polynomial can have

• The degree of a polynomial has no impact on the number of roots

Discuss the role of synthetic division in solving higher order polynomials.

• Synthetic division is only applicable to quadratic polynomials

• Synthetic division simplifies the process of dividing higher order polynomials by linear factors.

• Synthetic division is a method for finding the derivative of a polynomial function

• Synthetic division is used to multiply higher order polynomials

Tags

CCSS.HSA.APR.D.6

Explain the concept of multiplicity of roots in polynomial equations.

• Multiplicity of roots is the same as the degree of the polynomial equation

• Multiplicity of roots indicates the size of the roots in the solution set

• Multiplicity of roots in polynomial equations refers to the number of variables in the equation

• In polynomial equations, multiplicity of roots refers to the number of times a particular root appears in the solution set.

Tags

CCSS.HSF-IF.C.7C

Solve: -6x-1+5x²=8x²

• x = 5 ±√67 /6

• x = 1, 2/7

• x = 1 ±√ 22

• x = 3 ±√6 / -3

Tags

CCSS.HSA-REI.B.4B

Solve x⁴ - 256 = 0

• x = 4, x = - 4

• x = 4, x = 4i

• x = 4, x -4, x = 4i

• x = 4, x -4, x = 4i,         x = -4i

Tags

CCSS.HSA-REI.B.4B

• a = 0 (repeated)

• a = 1 (repeated)

• a = 1 (repeated), 0 (repeated)

• a = -1 (repeated), 0 (repeated)

Tags

CCSS.HSF-IF.C.7C

Answer explanation

The roots of the polynomial equation can be found by factoring the equation as (x-1)(x+2)(x-3)=0. Therefore, x = 1, -2, 3.

Tags

CCSS.HSA-REI.B.4B

What are the solutions to the polynomial equation?
Choose ALL that apply.

• 2

• -2

• -3

• 3

Solve the following equation 0 = x³ -3x²-5x+15

• 3, √5

• 3, √5, -√5

• -3, √5, -√5

• -3, 5i, -5i