Q 6.18 TI - Intermediate Algebra

Question

Factor $t^2+14t+24$

Step-by-Step Solution

Answer

The factored form is $(t+12)(t+2)$

Step 1: Given information

Given the polynomial $t^2+14t+24$

Step 2: Writing as parentheses

The polynomial can be written as $(t )(t )$. Now creating the table 

Factors of $24$	Sum of factors
$1,24$	$1+24=25$
$2,12$	$2+12=14$
$3,8$	$3+8=11$

Step 3: Use m , n as last terms of factors and form the factored polynomial

Here,

 $$\begin{gathered} m,n=12,2 \\ m+n=12+2 \\ m+n=14 \\ m\times n=12\times 2 \\ m\times n=24 \end{gathered}$$

Step 4: Substitute the values and form the polynomial

The polynomial is $(t+12)(t+2)$