Chapter 8.5, Problem 12PPE

To determine

To find:the missing term in factor of polynomial $t^2-10t+24=\left(t-4\right)\left(t-\boxed{}\right)$ .

Answer to Problem 12PPE

The missing constant is 6and the factor is $t^2-10t+24=\left(t-4\right)\left(t-\boxed{6}\right)$ .

Explanation of Solution

Given information:

The polynomial is $t^2-10t+24$ .

Calculation:

Factorize the polynomial as follows:

  $\begin{array}{c}{t}^2-10t+24=t^2-6t-4t+24\left(24t^2=\left(-6t\right)\left(-4t\right)\right)\\ =t\left(t-6\right)-4\left(t-6\right)\\ =\left(t-6\right)\left(t-4\right)\end{array}$

Thus, the missing constant is 6 and the factor is $t^2-10t+24=\left(t-4\right)\left(t-\boxed{6}\right)$ .