The complete factorization of 15x² - 6x + 5xy - 2y is (5x - 2)(3x + y)
Step-by-step explanation:
If we have an expression of four terms, then we factorize it by using
the grouping factorization
In grouping factorization we do that
1. Collect each two terms with common factors into 2 brackets
2. Take the common factor from each bracket, which make the brackets
equal each other
3. Take the bracket as a common factor, the answer will be 2 factors
multiply by each other
∵ The expression is 15x² - 6x + 5xy - 2y
- Take the first 2 terms in a bracket and the last 2 terms in another
bracket
∴ (15x² - 6x) + (5xy - 2y)
∵ The common factor of 15x² and 6x is 3x
- Divide each term by 3x
∵ 15x² ÷ 3x = 5x
∵ 6x ÷ 3x = 2
∴ (15x² - 6x) = 3x(5x - 2)
∵ The common factor of 5xy and 2y is y
- Divide each term by the common factor y
∵ 5xy ÷ y = 5x
∴ 2y ÷ y = 2
∴ (5xy - 2y) = y(5x - 2)
∴ (15x² - 6x) + (5xy - 2y) = 3x(5x - 2) + y(5x - 2)
∵ The bracket (5x - 2) is a common factor of the two terms
- Divide each term by the common factor (5x - 2)
∵ 3x(5x - 2) ÷ (5x - 2) = 3x
∵ y(5x - 2) ÷ (5x - 2) = y
∴ 3x(5x - 2) + y(5x - 2) = (5x - 2)(3x + y)
∴ 15x² - 6x + 5xy - 2y = (5x - 2)(3x + y)
The complete factorization of 15x² - 6x + 5xy - 2y is (5x - 2)(3x + y)
Learn more:
You can learn more about the factors in brainly.com/question/10771256
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