Question

Factor Trinomials of the form $x^2+bx+c$

$u^2+17u+72$

Short answer

Factor is:$u^2+17u+72=(u+8)(u+9)$

Step-by-step solution

Step 1. Given information

given expression$u^2+17u+72$

Step 2. Factor the expression by grouping. 

First, the expression needs to be rewritten as $u^2+au+bu+72$. To find $a$and $b$, set up a system to be solved.

role="math" localid="1647714934406" $$\begin{gathered} a+b=17 \\ ab=72 \end{gathered}$$

Step 3. Find a and b

by guessing all such integer pairs that give product 72.

we find,

$a=8,b=9$

Rewrite the expression localid="1647716094479" role="math" $u^2+17u+72\text{as}{u}^2+8u+9u+72$

Step 4. Now factor

$$\begin{gathered} u^2+8u+9u+72=\left(u^2+8u\right)+(9u+72) \\ =u(u+8)+9(u+8) \\ =(u+8)(u+9) \end{gathered}$$

Therefore, the factor of the given expression is$(u+8)(u+9)$