Finding Factors in Algebra

The factors of a term can be found.

A Simple Example of How to Find Factors in Algebra

Finding the factors of a term is easy. Find the factors of any numbers and of each letter and bracket that appears in the term.

Step-by-Step:

Answer:

The factors of 2x are:

A More Complicated Example of How to Find Factors in Algebra

Things get more complicated when there are exponents and brackets.

Step-by-Step:

Answer:

The factors of 4x²(y + 1) are:

Products of Factors Are Also (Usually) Factors

While 1, 2, 4, x, x², y + 1 and 4x²(y + 1) are all factors of 4x²(y + 1), they are not the only factors. Other factors can be found by multiplying these factors together. For example,

• 2 and x are factors, so 2x is also a factor.
• 4, x and y + 1 are factors, so 4x(y + 1) is also a factor.

Be careful, not all the products of these factors are factors For example,

• 2 and 4 are both factors, but their product 8 can not be a factor. Any product of number factors greater than the actual number in the term (4 in our example) can not be a factor.
• x and x² are both factors, but their product x³ can not be a factor. Any product of letters can not have an exponent greater than the exponent of the letter in the term (x² in our example).
• 4x²(y + 1) is the both a factor of the term and the term itself. It can not be multiplied by another other factor (apart from 1) to make another factor.

What Is a Factor in Algebra?

A factor is a quantity that divides exactly into a term. A factor is one of the numbers, letters and brackets (or a product of them) that are multiplied together to make a term.

Numbers Have Factors

A factor is a number which divides exactly into another number. For example, the factors of 4 are 1, 2 and 4 because they all divide exactly in 4. If an term in algebra includes a number, the factors of the number are also factors of the term. For example. the factors of 4xy are 1, 2, 4, x and y.

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