Factor the polynomial function to determine the x intercepts and the y intercept - y = x^5 - 21x^3 + 80x Enter the x intercepts in order from smallest to largest, then the y intercept.

llltkl | Student

Given that, `y = x^5 - 21x^3 + 80x`







For obtaining x-intercept, put y=0.

So, `x(x-4)(x+4)(x-sqrt5)(x+sqrt5)=0`

`rArr x=0,4,-4,sqrt5, and (–sqrt5).`

Arranging from smallest to largest,

`x=-4, (-sqrt5), 0, sqrt5, and 4.`

For obtaining y-intercept, put x=0.

Then `y=0(0-4)(0+4)(0-sqrt5)(0+sqrt5)=0`

Therefore, the x intercepts are` -4, (-sqrt5), 0, sqrt5, and 4` , and the y intercept is `0` .