Chapter 8.5, Problem 2GP

To determine

To factor: The polynomial $24t-16t^2$ and find the height of the kangaroo after 1 second

Answer to Problem 2GP

  $8t\left(3-2t\right)$

  $8\text{ inches}$

Explanation of Solution

Given:

The height of a kangaroo’s hop in inches after t seconds can be modelled as $24t-16t^2$

Calculation:

The Distributive Property is given by

  $a\left(b+c\right)=ab+ac\text{ and }ab+ac=a\left(b+c\right)$ , where a , b and c are real numbers

Now, in the given polynomial the GCF is $8t$

So, factored out the GCF and use the distributive property

  $\begin{array}{l}24t-16t^2\\ =8t\left(3-2t\right)\end{array}$

So, the factored form is $8t\left(3-2t\right)$

Now, substituting $t=1$ in the given model to find the height

  $\begin{array}{c}h\left(1\right)=24\left(1\right)-16{\left(1\right)}^2\\ =24-16\\ =8\end{array}$

Therefore, the height of the kangaroo’s hop after 1 second is $8\text{ inches}$