Chapter 4.6, Problem 4OE

To determine

To find the factor .

Answer to Problem 4OE

The required solution is, $t^2+11t+10=\left(t+1\right)\left(t+10\right)$ .

Explanation of Solution

Given information: The integer is, $t^2+11t+10$ .

Concept used: Factored completely.

A polynomial is factored completely when it is written as a product of factors and each factor is either a monomial, a prime polynomial, or a power of a prime polynomial.

Calculation: The required solution is obtained as,

  $\begin{array}{l}{t}^2+11t+10\\ =t^2+t+10t+10\\ =t\left(t+1\right)+10\left(t+1\right)\\ =\left(t+1\right)\left(t+10\right)\end{array}$

The polynomial is factored completely since $\left(t+1\right)$ and $\left(t+10\right)$ .

Hence, the required solution is, $t^2+11t+10=\left(t+1\right)\left(t+10\right)$