Factor Calculator

What is a Factor?

The integers are multiplied together to produce factors in multiplication. For instance, \( 7 × 2 = 14\). In this case, the factors of 14 are 7 and 2. Therefore, the components of 14 would also include 1, 2, 7, and 14.

The original numbers influence the product number. For example, a and b are factors of c if \( a × b = c \).

Basic Factorisation Formula

\( a^2 – b^2 = (a – b)(a + b) \)

\( (a + b)^2 = a^2 + 2ab + b^2 \)

\( (a – b)^2 = a^2 – 2ab + b^2 \)

\( a^3 – b^3 = (a – b)(a^2 + a b + b^2) \)

\( a^3 + b^3 = (a + b)(a^2 – ab + b^2) \)

\( (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \)

\( (a – b – c)^2 = a^2 + b^2 + c^2 – 2ab + 2bc – 2ca \)

Examples

Example 1: Let’s factor \(x^2 + 8x + 16\)

The middle number is 8 and the last number is 16.

For factoring them we want something like, (x + _)(x + _)

We need two numbers that add them together to get 8 and multiply together to get 16.

We will try 4 and 4:

\( 4 + 4 = 8 \)

\( 4 × 4 = 16 \)

Answer: \( (x + 4)(x + 4) \)

Example 2: Factorize \( x^3 − x^2 − 9x + 9 \)

First, we will factor the first two and second two separately:

\( x^2(x − 1) − 9(x − 1) \)

We see that (x-1) is on both, so let us use that:

\( (x^2 − 9)(x − 1) \)

And \( x^2 − 9 \) can be simplified as: \( (x – 3) (x + 3) \)

Answer: \( (x − 3)(x + 3)(x − 1)\)

FAQs