Remainder Theorem and Multiplicity

What is the remainder of (4x³ - 3x² - 4x +2) ÷ (x - 3)?

• -71

• 71

• 145

What is the remainder when x⁴ - 5 is divided by x + 3?

• 76

• 81

• 7

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

• 14

• -53

• 67

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

• YES
• NO

What is the remainder of  (3x³ -5x² -4x +1) ÷ (x + 3)?

• -25
• 25
• 113
• -113

Decide if (x-3) is a factor of 3x³+10x²-x-12

• Yes, it is a factor!
• No, it is not a factor!

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

• Yes
• No

Is (x-7) a factor of (x²-5x+14)?

• Yes
• No

• Yes, x-3 is a factor of p(x) since the remainder is 0.

• No, x-3 is not a factor of p(x) since the remainder is 0.