Problem
Understanding 8. Consider the expression $(x-1)^{2}+5(x-1)-6$ a. Substitute $w=x-1$ in this expression. b. Factorise the resulting quadratic. c. Replace $w$ with $x-1$ and simplify each factor. This is the factorised form of the original expression. TOPIC 7 Quadratic expressions 275
Solution
Step 1 ：Substitute \(w = x - 1\) in the given expression: \(w^2 + 5w - 6\)
Step 2 ：Factorise the resulting quadratic: \((w - 1)(w + 6)\)
Step 3 ：Replace \(w\) with \(x - 1\) and simplify each factor: \(\boxed{(x - 2)(x + 5)}\)
