Polynomial Remainder Theorem Practice

The video tutorial explains the polynomial remainder theorem, demonstrating how to find the remainder when a polynomial is divided by a linear divisor. It includes multiple examples, such as finding the remainder when dividing by x+3 and solving for an unknown integer when given a specific remainder. The tutorial also covers finding remainders for different divisors, emphasizing the importance of evaluating the polynomial at specific values to determine the remainder.

What does the polynomial remainder theorem help us determine?

• The coefficients of a polynomial

• The roots of a polynomial

• The remainder when a polynomial is divided by a linear expression

• The degree of a polynomial

When dividing a polynomial by x + 3, at which value should the polynomial be evaluated to find the remainder?

• 0

• -3

• 1

• 3

In the example where p(x) is divided by x - 2, what is the remainder?

• 0

• 2

• 3

• 1

What is the value of k if the remainder is 1 when p(x) is divided by x - 2?

• 5

• 2

• 3

• 4

When p(x) is divided by x + 4, what is the remainder?

• 0

• 1

• 2

• 3

What is the value of p(-4) if the remainder when divided by x + 4 is 3?

• 0

• 1

• 3

• 2

What is the remainder when p(x) is divided by x - 1?

• 3

• 2

• 1

• 0

What is the remainder when p(x) is divided by x - 3?

• 3

• 1

• 0

• 5

How do you find the remainder when dividing by x?

• Evaluate p(x) at x = -1

• Evaluate p(x) at x = 1

• Evaluate p(x) at x = 2

• Evaluate p(x) at x = 0

What is the value of p(0) if the remainder when divided by x is -1?

• -1

• 0

• 1

• 2