Question

Rewrite the following in a 5th graders response

The error in George's solution is that he factored the quadratic expression without setting the equation to zero first.
In Step 2, he incorrectly assumes that if
(x+5)(x-1) = 7, then x + 5= 0
and x - 1 = 0. This is only true when
the quadratic expression is equal to zero.
To correctly solve the equation, George should have first subtracted 7 from both sides of the equation to get
x^2+ 4x - 12 = 0. Then, he could have
factored the quadratic expression as
(x + 6) (x - 2) = 0, and set each factor
equal to zero to find the solutions
x=-6 and x = 2

Answer 1

George made a mistake. He factored before he made one side zero. You can only say “if A·B = 0 then A = 0 or B = 0” when the product equals 0. But George had (x+5)(x-1) = 7, so he can’t set x+5 = 0 and x-1 = 0.

Here’s the right way:
1. Subtract 7 from both sides: x^2 + 4x − 12 = 0.
2. Factor: (x + 6)(x − 2) = 0.
3. Set each factor to zero: x + 6 = 0 → x = −6, and x − 2 = 0 → x = 2.

Check: If x = 2, (2+5)(2−1) = 7·1 = 7. If x = −6, (−6+5)(−6−1) = (−1)(−7) = 7. Both answers work.