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 = 10*x+ x *= 11*x*. This
is not the middle term.
*x×*5 + *x×*2 = 5*x+ *2*x *= 7*x*.
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 9
##### Solution:
Multiply the numbers along the arms of the cross, and then add the
products.
*x×*14 + *x×*1 =
14*x+ x *= 15*x*.
We reject this pair as the middle term is 9*x*.
*x×*7 + *x×*2 = 7*x+ *2*x *=
9*x*.
We accept this pair as the middle term is 9*x*.
* x× *– 4 + *x× *–3 = – 4*x *– 3*x *= –7*x*.
We accept this pair as the middle term is –7*x*.
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 = –7*x
+ x *= –6*x*. We accept this pair as the middle term is –6*x*.
###### 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 |