Solve Higher Degree Polynomials

Level 2 Question 12
8x⁵-8x³+x²-1

• Prime

• (x+1)(x-1)(2x+1)(4x²-2x+1)

• (x+1)(x-1)(8x³ + 1)

• (x+1)(x-1)(2x+1)³

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

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

• 3, √5

• 3, √5, -√5

• -3, √5, -√5

• -3, 5i, -5i

What are the solutions for the polynomial equation

0 = 3 (x + 4) (x + 1) (x - 3)?

• -4, -1, 3

• 3, -3, 4, 1

• 4, 1, -3

• 3, -4, -1, 3

The function shown in the graph is:

• even

• odd

• neither even nor odd

• both even and odd

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

What is the equation of this graph in factored form?

• (x - 1)(x + 3)²

• (x - 1)²(x + 3)

• (x + 1)²(x - 3)

• (x + 1)(x - 3)²

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

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

• 5

• 4

• 3

• 2

What is the end-behavior of the function 
y = -x³ + 6x² + 7x

• as x-> -∞  f(x) -> ∞
   as x-> ∞  f(x) -> -∞

• as x-> -∞ f(x) -> ∞
   as x-> ∞  f(x) -> ∞

• as x->-∞ f(x) -> -∞
   as x-> ∞   f(x) -> ∞

• as x-> -∞ f(x) -> -∞
   as x-> ∞ f(x) -> -∞