Writing Polynomial Functions

Front

What are the zeros of the polynomial function y=(x + 2)(x - 3)(3x - 5)?

Back

The zeros are x = -2, x = 3, and x = \frac{5}{3}.

Front

What is the factored form of the polynomial function that has zeros at x = -4, x = -1 (multiplicity 2), and x = 2, x = 4?

Back

The factored form is f(x) = (x + 4)(x + 1)^{2}(x - 2)(x - 4).

Front

How many zeros does the polynomial function P(x) = 3x^4 + 4x - 8 have?

Back

The polynomial function has 4 zeros.

Front

What is the polynomial function represented by the graph with zeros at x = -3, x = -1, x = 2, and x = 5, and a leading coefficient of -2?

Back

The polynomial function is y = -2(x + 3)(x + 1)(x - 2)(x - 5).

Front

State the zeros of the polynomial f(x) = x(x + 3)^{2}(x - 2) including their multiplicities.

Back

The zeros are x = 0 (multiplicity 1), x = -3 (multiplicity 2), and x = 2 (multiplicity 1).

Front

What is the definition of a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What is the degree of the polynomial function f(x) = 2x^3 - 4x^2 + x - 7?

Back

The degree of the polynomial function is 3.

Front

What does it mean for a zero to have multiplicity?

Back

Multiplicity refers to the number of times a particular zero is repeated in a polynomial function.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros, set the polynomial equal to zero and solve for the variable.

Front

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

Back

The leading coefficient is 5.