Remainder Theorem

For the polynomial p(x), if p(3)=0, it can be concluded that ...

• x+3 is a factor of p(x)

• x-3 is a factor of p(x)

• when p(x) is divided by 3, the remainder is zero

• when p(x) is divided by -3, the remainder is zero

• -230

• 0

• 40

• 240

• 0

• 2

• 3

• -3

• (x-1) is a factor because P(-1)=2.

• (x+1) is a factor because P(-1)=2.

• (x+1) is a factor because P(1)=0

• (x-1) is a factor because P(1)=0

Given P(x) = x³ + x² – x ─ 9, what is the value of P (4)?

• 14

• -53

• 67

The expression x³ ─ kx² +2x +5 leaves a remainder of 2 when divided by x ─ 3. Find the value of k.

• 4

• -4

• 8

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

• Yes
• No

What is the remainder of (x³ - 5x² - 8x +1) ÷ (x + 1)?

• -13

• 1

• 3

Find the value of k given that when x³-2kx²+3x-1 is divided by x-1 the remainder is -3.

• 3

• -3

• 2

• 6