Polynomial Operations and Properties

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 examples and methods for each concept.

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

• 4

• 2

• 3

• 1

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

• Multiply them

• Subtract them

• Add them together

• Ignore them

What is the result of subtracting (3x^2 + 2x - 5) from (5x^2 - x + 3)?

• 2x^2 - 3x + 8

• 8x^2 + x - 2

• 8x^2 - 3x + 8

• 2x^2 - 3x - 2

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

• x

• 1

• x^3

• x^2

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

• x^2 + 1

• x^2 - 1

• x^2 + x

• x^2 - x

How many factors does a cubic polynomial have?

• 1

• 2

• 3

• 4

Which of the following is a factor of x^3 - x?

• x + 1

• x - 2

• x - 1

• x + 2

What is the remainder when 2x^3 - 3x^2 + 5x + 7 is divided by x + 2?

• -7

• 31

• 0

• -31

According to the remainder theorem, what is the remainder when a polynomial is divided by x - a?

• The leading coefficient

• Always zero

• The constant term

• The value of the polynomial at x = a

If p(x) = x^3 - x, what are the zeros of the function?

• -1, 1, 2

• -2, 0, 2

• 0, 1, 2

• -1, 0, 1