Quadratic expressions and equations

Choosing the correct factor pair but placing the signs wrongly, e.g. writing $(x+8)(x-3)$ for $x^2-5x-24$ instead of $(x-8)(x+3)$. Expand back to check: $(x+8)(x-3)=x^2+5x-24$, not $x^2-5x-24$.

After factorising in part (i), students asked to "hence solve" try to factorise again or use the quadratic formula instead of reading the roots from their factors — and some give factors when solutions were asked for (or vice versa).

When $a\ne 1$, the number inside the bracket must be multiplied by the leading coefficient. Writing $2x^2-24x+7=2(x-6)^2-36+7$ leaves $-36$ when it should be $2\times(-36)=-72$, i.e. $2(x-6)^2-72+7$. For a negative leading coefficient, take out the $-1$ (or $-3$) first.

In $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ the whole numerator is divided by $2a$, not by $2$. Watch the sign of $-b$ when $b$ is negative, keep the $\pm$, and rearrange properly to $=0$ first.

In the quadratic formula, do not round $\sqrt{b^2-4ac}$ until the final line. Rounding $\sqrt{73}$ to $8.5$ early shifts both roots; keep full accuracy, then round the answer to the required decimals.

Giving $(x-4)(x+3)$ when the question asked to solve. Set each bracket to $0$: $x=4$ or $x=-3$. A "solve" answer must be the values of $x$, not the factors.