Answer
$\text{D}$
Work Step by Step
We see that all three terms have a common factor: $x^2$. We can factor this out to get:
$$x^4-3x^3+2x^2=x^2(x^2 - 3x + 2)$$
We can further factor the polynomial inside the parentheses. This polynomial is in the form of the quadratic expression $x^2 + bx +c$. We look at the factors of $c$ such that when they are added together, they add up to $b$, meaning, we look at the factors for $2$ that add up to $-3$:
For factors $-2$ and $-1$:
$b =-2+(-1)= -3$
For factors $2$ and $1$:
$b = 2+1=3$
We see that the first set of factors work, so the factored form of the trinomial is:
$$x^2 -3x + 2$ = (x - 2)(x - 1)$$
Thus, $x^2(x^2-3x+2)=x^2(x - 2)(x - 1)$.
The correct answer is option $D$.
