1. The problem asks us to fully factorise the expression $20 + x - x^2$. 2. First, rewrite the expression in standard quadratic form: $$20 + x - x^2 = -x^2 + x + 20$$ 3. Factor out the negative sign to make the quadratic easier to factor: $$-x^2 + x + 20 = -(x^2 - x - 20)$$ 4. Now, focus on factorising the quadratic inside the parentheses: $x^2 - x - 20$. 5. We look for two numbers that multiply to $-20$ and add to $-1$ (the coefficient of $x$). 6. These numbers are $-5$ and $4$ because $-5 \times 4 = -20$ and $-5 + 4 = -1$. 7. So, we can factor the quadratic as: $$(x - 5)(x + 4)$$ 8. Therefore, the fully factorised form of the original expression is: $$-(x - 5)(x + 4)$$ This means the expression $20 + x - x^2$ can be written as $-(x - 5)(x + 4)$ after factorisation.