#45
Top 50 Mistake
Solving without setting equal to zero first
"The Zero Forgetter"
The Mistake in Action
Solve $x^2 + 3x = 10$
Wrong: $x(x + 3) = 10$ So $x = 10$ or $x + 3 = 10$, giving $x = 7$
Why It Happens
Students try to factorise before rearranging to equal zero. They wrongly apply the "if $ab = 0$ then $a = 0$ or $b = 0$" rule to non-zero products.
The Fix
The zero product rule only works when the product equals zero.
Correct method: $$x^2 + 3x = 10$$ $$x^2 + 3x - 10 = 0$$ $$(x + 5)(x - 2) = 0$$ $$x = -5 \text{ or } x = 2$$
Check: $(-5)^2 + 3(-5) = 25 - 15 = 10$ ✓
Spot the Mistake
Can you identify where this student went wrong?
Solve $x^2 + 3x = 10$
$x(x + 3) = 10$
$x = 10$ or $x = 7$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: