Remainder & Factor Theorem

If (x + 1) is a factor of 2 x ³ + a x ² + 2 bx + 1, then find the values of a and b given that 2 a – 3 b = 4

• a = –1, b = –2

• a = 2, b = 5

• a = 5, b = 2

• a = 2, b = 0

If 𝒙²+𝟑𝒙+𝟕 is divided by  𝒙+𝟐, then what is the remainder?

• 0

• -3

• 9

• 5

If dividing polynomial g(x) by (x – 1) yields a remainder of 2, which must be true?

• g(1) = 2

• g(-1) = 2

• g(2) = 1

• g(2) = -1

When dividing p(x) = x³ + 2x² + 3x - 10 by (x - 2) what is the remainder aka p(-2)? (shortcut: just plug in the opposite aka 2)

(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

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

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

• Yes

• No

Is (x-7) a factor of (x²-5x+14)?

• Yes

• No

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

• -1,-3,-3

• -1,-3,3/2

• 3,3,3

• -3,2/3,-1