Solving Polynomials Rational Root Theorem

Find all the real zeros of the function
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

• x = 1/2, -6

• x = -1/2, 6

• x = 4, -1/2, 6

• x = -4, 1/2, -6

x² + 12x + 32 = 0

• x = -4, 8

• x = 4, 8

• x = -4, -8

• x = 0, 12

Solve the trinomial:

12x²-12x - 24 = 0

• -1,2

• 1,2

• 1,-2

• -1,-2

Find all zeros for the polynomial
P(x) = x³ -3x²-5x+15

• 3, √5 

• 3, √5, -√5

• -3, √5, -√5

• -3, 5i, -5i

Solve 8x³ - 27 = 0

Find a polynomial function of degree 3 that has zeroes at
x=1, 2, and 3

• x³ - 6x² + 11x - 6

• x³ - 11x² - 6x - 6

• x³ - 6x² - 6x - 6

• x³ - 11x² - 11x - 11

Find a polynomial function that has zeroes at
x=1+√2, 1-√2, and 1

• x³ - 3x² + x +1

• x³ - 3x² + 3x +1

• x³ - x² + x +3

• x³ - 3x² + 3x +3

How many x-intercepts does x⁴+6x²+9= 0 have?

• 2

• 1

• 4

• None

Descartes' Rule of Signs is helpful is solving what kind of equation?

• rational

• exponential

• logarithmic

• polynomial

Use the Fundamental Theorem of Algebra to determine the total number of solutions.

• A

• B

• C

• D