Question

98 POINTS ASAP

You will need to factor this polynomial completely and show all of your work.

f(x)= x^4 -3x^3 - 5x^2 + 21x + 22

When you have all of the roots, sketch the graph on the coordinate grid shown below.

Answer 1

The rational root test leads to two roots of
`f(x)`,
`f(-1)=f(-2)=0`, which means both
`x+1` and
`x+2` are factors.

`(x^4 -3x^3 - 5x^2 + 21x + 22)/((x+1)(x+2))=x^2-6x+11`

The discriminant of the remaining quadratic is negative
`((-6)^2-4(11)=-8)` and so it has no real roots. So

`f(x)=(x+1)(x+2)(x^2-6x+11)`