Factors and Zeros of Polynomial Functions

Front

What are the x-intercepts of the polynomial function y = 2(x - 1)(x + 3)(x - 4)?

Back

1, -3, and 4

Front

Factor the polynomial 3x² - 75.

Back

3(x + 5)(x - 5)

Front

What is the maximum number of solutions for the polynomial f(x) = 5x⁴ + 2x³ + 2x - 7?

Back

4

Front

Convert the factored form y = (x + 1)(x - 3) to standard form.

Back

y = x² - 2x - 3

Front

What is the degree of the polynomial function graphed here if it has 5 turning points?

Back

5

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which the function f(x) = 0.

Front

How do you find the x-intercepts of a polynomial function?

Back

Set the polynomial equal to zero and solve for x.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have at most n real zeros.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its linear factors.