Factor the polynomial function to determine the x intercepts and the y intercept. Enter all of the x-intercepts from smallest to largest. Enter a rational answer as a fraction.
y = 4x^3 - 12x^2 - 9x + 27
The given polynomial is:
`y = 4x^3 - 12x^2 - 9x + 27`
By factoring, we get
`y = 4x^2(x-3) -9(x - 3)`
For x-intercepts, put y=0
Setting each factor equal to zero results in three solutions for x, viz.
`(x-3)=0 rArr x=3`
`(2x-3)=0 rArr x=3/2`
`(2x+3)=0 rArr x=-3/2`
Hence the x-intercepts of the given polynomial are -3/2, 3/2 and 3.
For y-intercept, put x=0
So, `y = 4*0^3 - 12*0^2 - 9*0 + 27`
Therefore, the y-intercept of the given polynomial is 27.