Fix the mistake: Factorization

Factoring ① Taking Out Common Factors

Factoring means transforming a polynomial into a product of several factors. First, let us learn how to find and take out common factors.

Taking out common factors

Find the factors, such as numbers or variables, common to each term, and take them outside the parentheses.
ma + mb = m(a + b)

📘 Example ①
Factor 6x² + 9x.
Answer:The common factor is 3x, so 6x² + 9x = 3x(2x + 3)
📘 Example ②
Factor 4a²b − 8ab².
Answer:The common factor is 4ab, so 4a²b − 8ab² = 4ab(a − 2b)
💡 Key points
  • Look for numbers and variables common to every term
  • Take out the greatest common factor of the coefficients
  • After taking out the factor, expand the expression in parentheses to check

Practice Problems

  1. Factor 12x² − 8x.
  2. Factor 6a²b + 15ab.

Answers and Explanations

  1. Answer:The common factor is 4x, so 4x(3x − 2)
  2. Answer:The common factor is 3ab, so 3ab(2a + 5)

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