Factoring: Common Factor in Evidence

Factoring appears as a resource in Mathematics to facilitate algebraic calculations; through it we can solve more complex situations.
In factoring by common factor in evidence, we use the idea of ​​making groups of polynomials, when factoring we write the expression in the form of product of simpler expressions.
the polynomial x² + 2x it has a factored shape, see:
x² + 2x.: we can say that the monomium x is common to all terms, so let's put it in evidence and divide each term of the polynomial x² + 2x per x.
We have: x (x + 2)
We concluded that x (x + 2) is the factored form of the polynomial x² + 2x.
To be sure of the calculations, we can apply the distribution in the expression x (x + 2) back to polynomial x² + 2x.
Examples of factoring using common factor in evidence:
Example 1
8x³ - 2x² + 6x (common factor: 2x)
2x (4x² - x + 3)
Example 2
The⁶ – 4a² (common factor: a²)
a² (The⁴ – 4)
Example 3
4x³ + 2x² + 6x (we noted that the 2x monomium is common to all terms)
2x (2x² + x + 3)
Example 4
6x³y³ - 9x²y + 15xy²

(common factor: 3xy)
3xy (2x²y² - 3x + 5y)
Example 5
8b⁴ – 16b² – 24b (common factor: 8b)
8b (b³ – 2b – 3)
Example 6
8x² - 32x - 24 (common factor: 8)
8 (x² - 4x - 3)
Example 7
3x² - 9xy + 6x + 21x³(common factor: 3x)
3x (x – 3y + 2 + 7x²)
Example 8
5a²b³c⁴ + 15 abc + 50 a⁴bc²(common factor: 5abc)
5abc (ab²c³ + 3 + 10a³ç)
Application of the common factor in evidence in solving a product equation (example 9) and in solving an incomplete 2nd degree equation (example 10).
Example 9
(3x - 2) (x - 5) = 0
We have:
3x - 2 = 0
3x = 2
x’ = 2/3
x – 5 = 0
x’’ = 5
Example 10
2x² - 200 = 0
We have:
2x² = 200
x² = 200/2
x² = 100
√x² = √100
x’ = 10
x’’ = – 10

by Mark Noah
Graduated in Mathematics
Brazil School Team

Algebraic Expression Factorization - Math - Brazil School

Source: Brazil School - https://brasilescola.uol.com.br/matematica/fator-comum.htm