Quiz on Dividing Polynomials

What happens when a numerical division has a remainder of zero?

• The divisor is not a factor of the dividend

• The divisor and quotient are both factors of the dividend

• The quotient is not a factor of the dividend

• The dividend is not divisible

What is the result when a polynomial division leaves no remainder?

• The polynomial is not factored

• The polynomial is multiplied

• The polynomial is factored

• The polynomial is divided again

• Yes

• No

• Only if x = 2

• Only if x = -2

What is the Remainder Theorem?

• If a polynomial \( P(x) \) of degree \( n \geq 1 \) is divided by \( (x - a) \), the remainder is \( P(a) \).

• If a polynomial \( P(x) \) is divided by \( (x + a) \), the remainder is zero.

• If a polynomial \( P(x) \) is divided by \( (x - a) \), the remainder is always one.

• If a polynomial \( P(x) \) is divided by \( (x - a) \), the remainder is \( a \).

• 172

• 160

• 0

• -172

• \( x + 1 \)

• \( x + 2 \)

• \( x + 3 \)

• \( x - 3 \)

• \( x(x + 1)(x + 6) \)

• \( x(x + 2)(x + 3) \)

• \( x(x + 3)(x + 2) \)

If a polynomial \( P(x) \) is divided by a binomial \( x - a \) and the remainder is zero, what conclusion can you draw?

• \( x - a \) is a factor of \( P(x) \)

• \( x - a \) is not a factor of \( P(x) \)

• The polynomial is prime

• The polynomial is zero

Which of the following, when multiplied by $ x - 1 $, results in a cubic polynomial whose standard form has three terms?

• $ x - 1 $