Factorization in mathematics is dividing a large number into smaller ones that, when multiplied together, give you the original number. The Mathematics Master Factor Calculator is used to find the positive or negative number's factors and factor pairs.
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 \( a × b = c \).
\( a^2 – b^2 = (a – b)(a + b) \)
\( (a + b)^2 = a^2 + 2ab + b^2 \)
\( (a – b)^2 = a^2 – 2ab + b^2 \)
\( a^3 – b^3 = (a – b)(a^2 + a b + b^2) \)
\( a^3 + b^3 = (a + b)(a^2 – ab + b^2) \)
\( (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \)
\( (a – b – c)^2 = a^2 + b^2 + c^2 – 2ab + 2bc – 2ca \)
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: \( (x − 3)(x + 3)(x − 1)\)
What is the greatest common factor?
Greatest Common Factor of 24 and 18
Alternatively, you can use an online greatest common factor calculator.
Find the greatest common factor of \( 9x^7 + 6x^4 − 3x^3\).
Given, \( 9x^7 + 6x^4 − 3x^3\)Now factoring in the given expression, we get;
\( = 3x^3 ( 3x^4 + 2x − 1 ) \)
Therefore, the greatest common factor is \( 3x^3 \).
What is a scale factor calculator?
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