Question

How do I factor this equation?
`{x}^(2) + 10x + 25`

Answer 1

Factorize:

`x^2+10x+25`
`\begin{gathered} \text{Step 1: Multiply the coefficient of x}^2\text{ and the constant term} \\ \text{The coefficient of x}^2\text{ in this case is 1 and the constant term is 25} \\ \text{ Therefore, 1 }*25\text{ = 25} \end{gathered}`
`\begin{gathered} \text{ Step 2: Find all the possible two-factor pairs of 25, obtained in step1 } \\ \text{The possible factors pairs are } \\ 1\text{ and 25} \\ 5\text{ and 5} \end{gathered}`
`\begin{gathered} \text{Step 3: Find the two-factor pairs of 25 that will sum up to give} \\ \text{ the coefficient of x which is 10} \\ \text{The desirable two-factor pairs is 5 and 5} \\ \text{ Because, 5+5 =10} \end{gathered}`
`\begin{gathered} \text{ Step 4: Substitute 10x for addition of the desirable pairs into the expression } \\ x^2+5x+5x+25 \\ \text{Factorize by grouping them} \\ (x^2+5x)+(5x+25) \\ x(x+5)+5(x+5) \\ =(x+5)(x+5) \end{gathered}`

Therefore, the factors of the

`x^2+10x+25\text{ = (}x+5)(x+5)`