Solve Equations with Polynomials

If the sum of (3x⁵ - 6x² + 8x + 5) and (3x⁴ + 7x³ - 7x² - 9x + 12) is subtracted from (3x⁵ + 8x⁴ - 8x + 15), the difference is...

If (x + 1) and (x + 3) are two factors of x³ - x² - 17x - 15, find the other one.

Find the cubic polynomial equation with roots -2, 2, and 4.

How many positive real roots does x⁴ - x³ - 11x² + 9x + 18 = 0?

• a = 0

• a = 2

• a = -2, 0

• a = 2, 0

-19 = -8 (-4 + a) - (2a + 1)

• a = -1

• a = 14

• a = -5

• a = 5

5.5 - Solving Polynomial Equations
Solve the equation.

• a = 0 (repeated)

• a = 1 (repeated)

• a = 1 (repeated), 0 (repeated)

• a = -1 (repeated), 0 (repeated)

Answer explanation

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

What are two solutions to the polynomial:
x²+14x=0

• x=0, x= 14

• x=-14

• x= 1, x =10

• x= -14, x = 0 

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

• 2

• -2

• -3

• 3