Remainder and Remainder Theorem

What is the remainder when      a³ - 4 is divided by a+2? 

• -2

• -6

• -12

• 0

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

• Yes

• No

(x – r) is a factor of P(x) if and only if __________.

• P(r) ≠ 0

• P(r) = 1

• P(r) = 0

• P(r) has two negative roots

Find the remainder when
P\left(x\right)=x^4+x^3-2x^2+4x-5 is divided by \left(x+3\right) .

• 19

• 20

• 21

• 22

4x⁴+4x³-9x²-x+2 ÷ x-1

• 4x³+8x²-7x-2

• 4x³+19x²-x-2

• 4x³+8x²-x-9

• 4x³+8x²-x-2

If x - 2 is NOT a factor of (2x³ - 5x - 7), what is the remainder?

• -13

• 2x³ + 4x² +3x - 1

• 13/x-2

• -1/x-2

find the value of k when x³-2kx²+3x-1 is divided by x-1 and the remainder is -3

• 3

• -3

• 2

• 6

We know f(4) = 0 for f(x)= x³-6x²+5x+12. Factor f(x) completely using this information.

• (x-4)(x+1)(x-3)

• (x-4)(x+1)(x+3)

• (x-1)(x-4)(x-3)

• (x+1)(x+4)(x+3)

Is (x + 2) a factor of the polynomial: x⁴ + x³ - 2x² + 3x + 7, and what was the remainder?

• no, R=1

• yes, R=0

• no, R=29

• yes, R=5

Divide

(n² + 10n + 18) by (n + 5)

• n + 4 Remainder of 2

• n - 7 Remainder of 5

• n + 5 Remainder of -7

• n + 1 Remainder of 0