Understanding the Polynomial Remainder Theorem

What is the remainder when dividing the polynomial 3x^2 - 4x + 7 by x - 1?

• 1

• 0

• 6

• 3

In polynomial long division, when do you know you have reached the remainder?

• When the quotient is a constant

• When the degree of the remainder is less than the divisor

• When the remainder is zero

• When the divisor is larger than the dividend

How is traditional division similar to polynomial division?

• Both require factoring

• Both result in a remainder

• Both involve multiplying by zero

• Both use the quadratic formula

What is the general form of a polynomial f(x) when divided by x - a?

• f(x) = q(x) + r

• f(x) = q(x) * r

• f(x) = q(x) * (x - a) + r

• f(x) = (x - a) * r

What happens to the term q(a) * (a - a) in the polynomial remainder theorem?

• It becomes a constant

• It equals zero

• It equals the remainder

• It equals the quotient

What is the polynomial remainder theorem primarily used for?

• Finding the roots of a polynomial

• Determining the degree of a polynomial

• Calculating the remainder when a polynomial is divided by a linear factor

• Solving quadratic equations

What is the degree of the remainder when dividing by x - a?

• First degree

• Second degree

• Zeroth degree

• Same as the divisor

What is the value of f(a) according to the polynomial remainder theorem?

• The product of the quotient and divisor

• The quotient

• The divisor

• The remainder

Why is the polynomial remainder theorem considered simple?

• It involves complex calculations

• It provides a straightforward proof

• It requires no division

• It is only applicable to linear polynomials

What is the main takeaway from the polynomial remainder theorem?

• It simplifies polynomial multiplication

• It relates the value of a polynomial at a point to its remainder

• It proves all polynomials are divisible by x - a

• It shows the remainder is always zero