Answer
-2 and 1 of multiplicity one
0 of multiplicity two
See graph below.
Work Step by Step
The question asks for all real zeros of P(x), their respective multiplicities, and the graph of P(x)
Given $P(x) = x^4 +x^3 -2x^2$
$P(x) = x^2(x^2 + x - 2)$
$P(x) = x^2(x+2)(x-1)$
Set $P(x) = 0$
Thus x = -2, 0, 1
To determine multiplicity, it is the power of the root determined from setting P(x) = 0
So -2 and 1 of multiplicity one
0 of multiplicity two
See graph below.
