1. Problem: Factorise $w^2 - 5w$. Step 1: Identify the common factor in both terms, which is $w$. Step 2: Factor out $w$ from each term: $$w^2 - 5w = w(w - 5)$$ The given factorisation $w(w + 5)$ is incorrect because the sign inside the parentheses should be negative. 2. Problem: Factorise completely $24x^2 + 20x$. Step 1: Find the greatest common factor (GCF) of $24x^2$ and $20x$, which is $4x$. Step 2: Factor out $4x$: $$24x^2 + 20x = 4x(6x + 5)$$ The given factorisation $4(6x^2 + 5x)$ is incorrect because it does not factor out the variable $x$. 3. Problem: Factorise completely $20a^2c + 30ac$. Step 1: Find the GCF of $20a^2c$ and $30ac$, which is $10ac$. Step 2: Factor out $10ac$: $$20a^2c + 30ac = 10ac(2a + 3)$$ The given factorisation $5ac(4a^2 + 6)$ is incorrect because the factors inside the parentheses are not simplified and the GCF is underestimated. Final answers: 1. $w(w - 5)$ 2. $4x(6x + 5)$ 3. $10ac(2a + 3)$