Why does my child write (2x + 3)(x + 1) for 2x² + 7x + 3?
Your child chooses brackets that give the first and last terms but the wrong middle term, such as (2x + 3)(x + 1) for 2x² + 7x + 3, which is (2x + 1)(x + 3).
Why children do it
With a number in front of x², the first and last terms come out right from many different brackets, and only one pair gives the middle term. (2x + 3)(x + 1) gives 2x² + 5x + 3; swapping the numbers over, (2x + 1)(x + 3), gives 7x. Multiplying each try back out finds the right one.
How to help at home
Ask them to multiply their brackets back out: is the middle term right as well as the first and last?
The right way
Factorise: 2x² + 7x + 3
- 2 × 3 = 6Multiply the first and last numbers.
- 1 × 6 = 61 and 6 multiply to 6 and add to 7, the middle number.
- 2x² + x + 6x + 3Split the middle term with them.
- x(2x + 1) + 3(2x + 1)Factorise each pair.
- (2x + 1)(x + 3)Take out the bracket they share.
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