Question

Factor completely 15x2 - 6x + 5xy – 2y

Answer 1

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)

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