End Behavior & Zeros of Polynomials

Front

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

Back

-4, -1, 3

Front

What is the degree of the polynomial f(x) = 7x^3 – 8x^2 + 9?

Back

3

Front

What is the factored form of the function f(x) = x³ + 7x² - 2x - 14?

Back

f(x) = (x² - 2)(x + 7)

Front

Find and select each real zero and its multiplicity for f(x) = x²(x - 2)³(x - 7).

Back

0 (Mult of 2), 2 (Mult of 3), 7 (Mult of 1)

Front

What are the zeros of the polynomial function y = x(x - 6)(x + 5)?

Back

0, 6, -5

Front

Define 'zero of a polynomial'.

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.

Front

What is the end behavior of a polynomial function of even degree?

Back

As x approaches ±∞, the function approaches ±∞.

Front

What is the end behavior of a polynomial function of odd degree?

Back

As x approaches -∞, the function approaches -∞; as x approaches +∞, the function approaches +∞.

Front

How do you determine the multiplicity of a zero?

Back

The multiplicity of a zero is determined by the exponent of the factor in the polynomial.

Front

What does it mean if a zero has an even multiplicity?

Back

If a zero has an even multiplicity, the graph touches the x-axis at that zero but does not cross it.