Question

Find the product of the equation y=x^2-6x+5 using any model

Answer 1

$y=x^2-6x+5$

Using the factorization model,

$\begin{gathered} \text{step 1: Multiply the coefficient of x}^2,\text{ 1 and the constant term 5.} \\ \text{Therefore, 1}\times5=5 \end{gathered}$$\begin{gathered} \text{Step 2: List the factor pairs of the product 5} \\ \text{The factor pairs are 1 and 5, -1 and -5} \end{gathered}$

$\begin{gathered} \text{Step 3: Determine the factor pair that adds up to }-6 \\ The\text{ coefficient of x}^{}\text{ is -6.} \\ \text{Therefore, the required factor pair will be -1 and -5, } \\ Because\text{ they sum up to -6} \end{gathered}$$\begin{gathered} \text{step 4: Substitute -1 and -5 for -6 }in\text{ the equation} \\ y=x^2-6x+5 \\ y=x^2-x-5x+5 \\ \end{gathered}$$\begin{gathered} \text{Step 5: Group the first two terms and the last two terms together}, \\ \text{then factorize completely} \\ y=x^2-x-5x+5 \\ y=x(x-1)-5(x-1) \\ y=(x-1)(x-5) \\ \end{gathered}$

The product of the equation is y = (x-1)(x-5)