Why Factor?

Factoring Unit. Lesson #2:

Objectives: Students will be able to explain what factoring is, why converting sums to products is important, and 3 general purposes for which factoring is commonly used.

NCTM Standards:Mathematics should make sense to students; they should see it as reasoned and reasonable. Their experience in school should help them recognize that seeking and finding explanations for the patterns they observe and the procedures they use help them develop deeper understandings of mathematics.

Factoring is expressing a sum as a product.

Factor 10 10 = 5 x 2

Factor 10 10 = 5 x 2

Divide 10 ÷ 510 ÷ 5 = 2

Divide 10 ÷ 210 ÷ 2 = 5

Factor 10 10 = 5 x 2

Multiply 5 x 25 x 2 = 10

What Is Factoring?

10 = 5 x 2 12 = 4 x 3 24 = 4 x 3 x 2

Factoring is like multiplication in reverse, because a product is given, and we are asked to find its multiplicands.

Example:

Example:

Factoring is also like division in reverse, because a dividend is given, and we are asked to find its quotients and divisors.

Example:

4 is the sum of 4 ones; 12 is the sum of 1 ten and 2 ones, etc.

Why Factor? (A)

Reason #1:

Example:

1

6

2

2

12

62

Factoring makes it possible to reduce fractions.

2

39

it is in.

This fraction cannot be reduced in the form

12

62

2

12

and factor , then it can, because

the rules of multiplication and division allow us to do this:

The rules of arithmetic make it possible to perform some operations on numbers that are multiplied or divided that cannot be performed on numbers that are added or subtracted.

2

12

2

39

But if we add the numbers in the numerator

Summary

We will come back to the distributive property "in reverse" and all of the other features of factoring as it applies to algebra after we have looked more closely at how factoring numbers works.

Factoring makes reducing, adding, and subtracting both numeric and algebraic fractions possible.

Factoring can be used to simplify algebraic expressions.

Factoring can be used to solve equations.

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