F.2 Mathematics: factorization by cross method

Factorize

.

By using the cross method, students may give the following two ‘possible answers’.

A.
B.

The correct answer is B. Some students may opt for A because the expression in A could give (so-called) the middle term . However, the constant term in A is (not , the correct one), hence A is not the answer.

Setting this type of question may remind students of the importance of checking the constant term.

Other examples like

=

A.
B.

=

A.
B.

Correct answers to the above are B. But some students may get it wrongly.

To set up such kind of questions, just consider two expressions:

All we need is setting

and

Yield

– – – – – – (*)

Then, we may put different positive integral value of and evaluate and finally .

Just give an example.

Put (say), by (*),

Just take and , thus

and hence

Hence we have two expressions

having the same ‘middle terms’ with constant terms differing in sign.

Of course, this article is rubblish once we have set program in calculators.