Polynomial and Rational Relationships

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

Factor:
 x³-12x²+47x-60=0 when 5 is a root.

• (x-3)(x-4)(x-5)=0
• (x+1)(x-4)(x-5)=0
• (x-3)(x-4)(2x-5)=0
• (x-5)(x-4)(x-5)=0

Find the roots of 0=x³-4x²+2x-8

• ±2,4
• ±2i,4
• ±i√2,4
• ±√2,4

Find all rational zeros, one zero has been given.
f(x) = x³-3x²-x+3;   3

• 2,4,3
• -1,1,3
• 3,2,1
• 4,5,6

One zero of 4x³-17x²-150x-189 is 9.
What is another zero?

• 4
• 7
• -3
• -6

Write the polynomial in standard form given the following zeros. x = -2, 1, 4

• f(x) = (x+2)(x-1)(x-4)

• f(x) =x³ - 3x² - 6x + 8

• f(x) = x³ + 8

• f(x) = x³ - 3x² + 8

Which of the following would be the correct factored form with roots 2, 5i, and 6?

• (x-6)(x-2)(x+5i)(x-5i)

• (x+6)(x+2)(x+5i)

• (x-6)(x-2)(x-5i)

• (x+6)(x+2)(x-5i)

If a+bi is a root of a polynomial, then _______ is also a root.

• i²

• a-bi

• a+bi

• -i²

Use the Complex Conjugate Root Theorem to state another complex solution. Given that -2-5i is a root. 

• -2-5i
• -2+5i
• 2+5i
• 5i

Find a polynomial function of degree 3 with zeros 3i and -2.

• P(x) = x³+2x²+9x+11
• P(x) = x³-2x²+9x+18
• P(x) = x³+2x²+9x+18
• P(x) = x²-3ix+2x-6i