For the following polynomial function, find A) the degree of the polynomial, B) all x-intercepts, and C) the y-intercepts? f(x)=(x^2-25)(x^2-9)

1 Answer
Jun 5, 2018

This is a fourth-degree polynomial

X-intercepts are - 5, -5, 3, and -3

The Y-intercept is 225

Explanation:

Since it's already in the factored form you can find the zeros by separating each binomial and solving for x

x^2-25=0x225=0
x^2=25x2=25
x=+-5x=±5

x^2-9=0x29=0
x^2=9x2=9
x=+-3x=±3
so x= +-5, +-3x=±5,±3

To find the y-intercept and the degree of the polynomial we need to convert the factored form into standard form

f(x)=(x^2-25)(x^2-9)f(x)=(x225)(x29)
f(x)=x^4-9x^2-25x^2+225f(x)=x49x225x2+225
f(x)=x^4-34x^2+225f(x)=x434x2+225

The degree of a polynomial is just the leading coefficients power which is 4 in this equation

In order to find the y-intercept we just need to allow x=0x=0 because that is when any equation will cross the y-axis

f(x)=0^4-34(0)^2+225f(x)=0434(0)2+225
f(x)=225f(x)=225