Polynomial & Rational Functions Review

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

How could you determine    if x-2 is a factor of 2x³-5x²+x-2?

• Use synthetic division and see if the quotient is even
• Ask the person sitting next to me
• Use synthetic division and see if the remainder is zero
• Flip a coin

Is (x-4) a factor of the polynomial x³-4x²+5x-20

• Yes
• No

Simplify the rational expression.

• (m+6)/(m-3)
• 7/(m-3)
• 7(m+6)
• (m-3)

Simplify the rational expression.

• (x+6)/(x+4)
• (x+6)(x+4)
• (x+6)
• (x+6)/(x-5)

Simplify the rational expression.

• (x-9)/(x+9)
• 1/(x-9)
• (x+9)
• 1/(x+9)

Solve for x. *Check for extraneous solutions.

• -1
• 2
• 6
• No solution

State the domain restrictions (excluded values). *think extraneous solutions.

• x ≠ -2
• x ≠ 2, 1
• x ≠ 2, -1
• x ≠ -2, 2, 1

Solve for x.

• 2
• 18/5
• 26/5
• 6