Polynomial Remainder and Factor Theorems

Front

What is the Polynomial Remainder Theorem?

Back

The Polynomial Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of this division is equal to f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

Determine if (x - 1) is a factor of 5x^4 - 2x^3 + 3x - 6.

Back

Yes, because f(1) = 5(1)^4 - 2(1)^3 + 3(1) - 6 = 0.

Front

What does the degree of a polynomial indicate?

Back

The degree of a polynomial indicates the maximum number of x-intercepts and the number of turning points.

Front

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

Back

Degree: 6, because the degree is the sum of the exponents.

Front

What are the zeros of the polynomial y = 3(x + 4)(x + 1)(x - 3)?

Back

The zeros are -4, -1, and 3.

Front

What is the remainder when x^2 - x - 6 is divided by x - 4?

Back

The remainder is 6.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

Front

What is the leading coefficient of the polynomial 4x^3 - 2x^2 + 5?

Back

The leading coefficient is 4, which is the coefficient of the term with the highest degree.