1.3.2 Factoring of Numerical Problems

In many of the intermediate problems, there are several examples where factoring can make the problem a lot easier. Outlined in the next couple of tricks are times when factoring would be beneficial towards calculation. We’ll start off with some standard problems:

$$21^2 + 63^2 = 21^2 + (3 \cdot 21)^2$$ $$= 21^2 \cdot (1 + 9)$$ $$= 4410$$

This is a standard trick of factoring that is common in the middle section of the test. Another factoring procedure is as followed:

$$48 \times 11 + 44 \times 12 = 11 \cdot (48 + 4 \times 12)$$ $$= 11 \cdot (96)$$ $$= 1056$$

Factoring problems can be easily identified because, at first glance, they look like they require dense computation. For example, the above problem would require two, two-digit multiplication and then their addition. Whereas when you factor out the 11 you are left with a simple addition and a multiplication using the 11’s trick.

Another thing is that factoring usually requires the knowledge of another trick. For instance, the first problem required the knowledge of a square ($21^2$) while the second example involved applying the 11’s trick.

The following are examples when factoring would lessen the amount of computations:

Problem Set 1.3.2