Polynomial Functions Zeros and Y-Intercepts

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18 Questions

The graph will cross the x-axis at zeros with ______ multiplicities. The sum of the multiplicities is the degree of the polynomial function.

odd

The right end rises. The left end ______.

falls

The possible rational roots of the polynomial function are the form where ______ is the set of all factors of $a$ and ______ is the set of all factors of $b$.

$p$, $q$

The roots of the polynomial function are ______ and ______.

-10, 10

The leading coefficient of the polynomial function is ______.

positive

The degree of the polynomial function is ______.

3

The end behaviors of the polynomial function are: Left - Rises / Up, Right - Rises / Up, degree – 1 = ______.

5

The zeros of the polynomial function are: $x=-1$, $x=2$, ______ $x=5$.

and

The y-intercept of the polynomial function is: $x=0$, $y=______$.

10

The number of turning points of the polynomial function is: ______.

1

The leading coefficient of the polynomial function is 1, indicating that the function ______.

rises

The polynomial function has a degree of 6, making it an ______ function.

even

Exercise 2.6 A Exercise 2.6 B 1. The zeros and y-intercept of a polynomial function can be found by solving the equation ______

P(x) = (x+2)(x-4)^3

Exercise 2.6 A Exercise 2.6 B 2. To find a polynomial function with zeros at 1, -2, and 3, the equation would be ______

P(x) = (x-1)(x+2)(x-3)

Exercise 2.6 A Exercise 2.6 B 3. A polynomial function with zeros at 2 and -1, each with a multiplicity of 3, would be represented by the equation ______

P(x) = (x-2)^3(x+1)^3

Exercise 2.6 A Exercise 2.6 B 4. The graph of a polynomial function will touch the x-axis at zeros with ______ multiplicities

even

Exercise 2.6 A Exercise 2.6 B 5. The zeros of the polynomial function P(x) = (x+2)(x-4)^3 are ______ and ______

-2 and 4

Exercise 2.6 A Exercise 2.6 B 6. The zeros of the polynomial function P(x) = (x-1)(x+2)(x-3) are ______, ______, and ______

1, -2, and 3

This quiz covers polynomial functions, including finding zeros and y-intercepts, determining multiplicities, and analyzing end behavior. It includes exercises to practice factoring and solving polynomial equations.

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