Polynomial Zeros

Front

What is the end behavior of a polynomial function with a leading coefficient that is negative and an even degree?

Back

The end behavior will fall on both sides.

Front

How do you determine the zeros of a polynomial function?

Back

Set the polynomial equal to zero and solve for x.

Front

What does it mean for a zero to have a multiplicity greater than 1?

Back

It means that the zero is repeated that many times in the factorization of the polynomial.

Tags

CCSS.HSF-IF.C.7C

Front

What is the significance of the leading coefficient in determining the end behavior of a polynomial function?

Back

The leading coefficient determines whether the ends of the graph rise or fall as x approaches positive or negative infinity.

Front

How can you express a polynomial function in factored form?

Back

By expressing it as a product of its linear factors.

Tags

CCSS.HSA.APR.B.2

Front

What are the zeros of the polynomial function f(x) = 3x(x - 4)(x + 5)?

Back

The zeros are -5, 0, and 4.

Tags

CCSS.HSF-IF.C.7C

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 up to n zeros.

Front

How do you find the multiplicity of a zero in a polynomial function?

Back

By examining the exponent of the factor associated with that zero in the factored form of the polynomial.

Tags

CCSS.HSF-IF.C.7C

Front

What is the general form of a polynomial function?

Back

f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n ≠ 0.

Front

What does the graph of a polynomial function look like at a zero with an odd multiplicity?

Back

The graph will cross the x-axis at that zero.