1. The problem is to fully factorise the quadratic expression $20 + x - x^2$. 2. First, rewrite the expression in standard quadratic form: $$20 + x - x^2 = -(x^2 - x - 20)$$ 3. Now, focus on factorising the quadratic inside the parentheses: $x^2 - x - 20$. 4. To factorise $x^2 - x - 20$, find two numbers that multiply to $-20$ and add to $-1$ (the coefficient of $x$). 5. The numbers are $-5$ and $4$ because $-5 \times 4 = -20$ and $-5 + 4 = -1$. 6. So, factor the quadratic as: $$x^2 - x - 20 = (x - 5)(x + 4)$$ 7. Substitute back into the original expression: $$20 + x - x^2 = -(x - 5)(x + 4)$$ 8. Therefore, the fully factorised form is: $$-(x - 5)(x + 4)$$