Question

1. the volume, v(h), of a bookcase can be represented by the expression h³ - 2h² + h, where h is the height of the bookcase. what are the possible dimensions of the bookcase in terms of h?

Explanation:

Step1: Factor the volume expression

We have $V(h)=h^{3}-2h^{2}+h$. First, factor out the common factor $h$: $V(h)=h(h^{2}-2h + 1)$.

Step2: Factor the quadratic expression

The quadratic $h^{2}-2h + 1$ is a perfect - square trinomial. Using the formula $(a - b)^2=a^{2}-2ab + b^{2}$, where $a = h$ and $b = 1$, we get $h^{2}-2h + 1=(h - 1)^2$. So, $V(h)=h(h - 1)(h - 1)$.

Answer:

The possible dimensions of the bookcase are $h$, $h - 1$, and $h - 1$.