Place the linear factors one above the other as shown below.
Multiply the numbers along the arms of the cross, and then add the
products. That is,
x×10 + x×1 = 10x+ x = 11x. This
is not the middle term.
x×5 + x×2 = 5x+ 2x = 7x.
This is the middle term.
Note:
- The solution is read across.
- 10 = 1 × 10 = 2 × 5 = –1 × –10 = –2 ×
–5
We did not try –1 × –10 and –2 × –5
because the middle term is positive.
- The answer can be checked using the Distributive
Law. That is:
Example 13
Factorise the following:
Solution:
Multiply the numbers along the arms of the cross, and then add the
products.
x×15 + x×1 = 15x+ x = 16x. This
is not the middle term.
We reject this pair as the middle term is 8x. Now, try the
next pair.
x×5 + x×3 = 5x+ 3x = 8x.
We accept this pair as the middle term is 8x.
x× – 4 + x× –3 = –
4x – 3x = –7x.
We accept this pair as the middle term is –7x.
Note:
We did not try 1 × 12, 2 × 6 and 3 × 4 because the middle term is
negative. Also, we did not try
–2 × –6 and –1 × –12 because we have
already obtained the middle term by using –3 × – 4.
x × 7 + x × –1 = 7x – x =
6x. We accept this pair as the middle term is 6x.
Note:
We did not try 1 × –7
because we have already obtained the middle term by using –1 ×
7.
Note:
We did not try –1 × 8, –2 × 4 and 2 × – 4
because we have already obtained the middle term by using 1 × –8.
Key Terms
cross-multiplication method
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