Question

Complete the factoringx² - 13x + 42x2 - 13x + 42 = (x-7)(O

Answer 1

Step-by-step explanation:
`\begin{gathered} Given: \\ x^2\text{ - 13x + 42} \end{gathered}`

To factorise, we need to find the factors of 42 whose sum gives -13:

`\begin{gathered} 42\text{ = 6 and 7} \\ -6\text{ }*\text{ -7 = 42} \\ -6\text{ - 7 = -13} \\ \\ x^2\text{ -6x - 7x + 42 = 0} \end{gathered}`
`\begin{gathered} x(x\text{ - 6\rparen -7\lparen x -6\rparen = 0} \\ (x\text{ - 7\rparen\lparen x - 6\rparen = 0} \\ x\text{ - 7 = 0 or x - 6 = 0} \end{gathered}`
`\begin{gathered} The\text{ complete factoring:} \\ x^2\text{-13x + 42 = \lparen x - 7\rparen\lparen x - 6\rparen} \end{gathered}`