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

Answer

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Answer

Replace $w$ with $x - 1$ and simplify each factor: $\boxed{(x - 2)(x + 5)}$

Steps

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: $\boxed{(x - 2)(x + 5)}$