Polynomial Operations and Theorems

The video tutorial covers polynomial functions, explaining their degrees and types. It demonstrates operations like addition, subtraction, and division of polynomials, including the remainder theorem. The tutorial also explores factorization and finding zeros of polynomial functions, providing practical examples to solidify understanding.

What is the degree of the polynomial f(x) = 4x^2 - 3x + 5?

• 1

• 2

• 3

• 4

When adding polynomials, what should you do with like terms?

• Multiply them

• Subtract them

• Ignore them

• Add them together

What is the result of adding the polynomials 7x^2 + 3x - 9 and 9x^2 - 3x - 15?

• 16x^2 + 24

• 9x^2 - 24

• 16x^2 - 24

• 7x^2 - 24

In polynomial division, what do you multiply x by to get x^3?

• x

• x^2

• 1

• x^3

What is the quotient when dividing x^3 - x by x + 1?

• x^2 + 1

• x^3 - x

• x^2 + x

• x^2 - x

How many factors does a cubic polynomial have?

• 1

• 4

• 2

• 3

What are the zeros of the function x^3 - x?

• -1, 0, 1

• 0, 1, 2

• -1, 1, 2

• 0, -1, 2

What does the remainder theorem help you find?

• The zeros of a polynomial

• The factors of a polynomial

• The remainder of a polynomial division

• The degree of a polynomial

If p(x) = 2x^3 - 3x^2 + 5x + 7, what is the remainder when divided by x + 2?

• 0

• 31

• -1

• -31

What is the first step in using the remainder theorem?

• Divide the polynomial

• Factor the polynomial

• Substitute the value into the polynomial

• Multiply the polynomial