Remainder and Rational Root Theorem

Is (x-4) a factor of (x³ +x² -16x-16)?

• YES
• NO

Is (x-3) a factor of
(x³ - 3x² + 2x + 2)?

• Yes
• No

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

• 2x³ - x² + x + 9

• 2x² - x + 1

• 2x² - x + 1 + 9/(x-2)

• 2x² - 9x - 15 - 23/(x-2)

What is the remainder when x³ - 4 is divided by x+2?

• -2

• -6

• -12

• 0

State the roots of the polynomial: x³ + 11x² + 24x.

• 8, 3

• -8, -3

• 0, 8, 3

• 0, -8, -3

State the roots of the polynomial: x³ - 4x² - 45x.

• 0, 9, 5

• 0, 9, -5

• 0, -9, 5

• 0, -9, -5

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

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

Find all roots of the polynomial:

x³ + 3x² - 6x - 8 = 0

• -4, -1, 2

• -4, -1, ±√2

• 1, 2, 4

• 4,-1,√2