Which statements about the factors of the terms in the expression 20 a + 15 a b + 24 b are true? Select three options.

The factors common to 20a and 15ab are 1, 5, a, and b.
The factors common to 20a and 15ab are 1, 5, and a.
The factors common to 20a and 24b are 1, 2, and 4.
The GCF of the expression is ab.
The GCF of the expression is 1

1 answer

To analyze the expression \(20a + 15ab + 24b\), let's break it down and identify the greatest common factors (GCF).

  1. Factors of each term:

    • 20a: The factors are \(1, 2, 4, 5, 10, 20, a\).
    • 15ab: The factors are \(1, 3, 5, 15, a, b\).
    • 24b: The factors are \(1, 2, 3, 4, 6, 8, 12, 24, b\).
  2. Common factors:

    • Between \(20a\) and \(15ab\): The common factors are \(1, 5, a\).
    • Between \(20a\) and \(24b\): The common factors are \(1, 2, 4\).
  3. Finding the GCF:

    • The GCF for the entire expression \(20a + 15ab + 24b\) is determined by identifying the common factors among all terms. The common factors for all three terms include \(1\) (as all coefficients have \(1\) as a factor), but there is no other factor common to all terms. Therefore, the GCF of the entire expression is 1.

Therefore, the true statements are:

  1. The factors common to \(20a\) and \(15ab\) are \(1, 5, a\).
  2. The factors common to \(20a\) and \(24b\) are \(1, 2, 4\).
  3. The GCF of the expression is \(1\).

The chosen correct options are:

  • The factors common to \(20a\) and \(15ab\) are \(1, 5,\) and \(a\).
  • The factors common to \(20a\) and \(24b\) are \(1, 2,\) and \(4\).
  • The GCF of the expression is \(1\).
Similar Questions
  1. Consider the following expression7u+2+4v Select all of The true statements A. 7u+2+4v is written as a product of three factors
    1. answers icon 1 answer
  2. What does it mean to factor an algebraic expression into prime factors?Prime factors are factors that cannot be further
    1. answers icon 0 answers
  3. Key terms:Expression Terms Factors Coefficients Meaning - definition - picture - Example with problems showing all steps
    1. answers icon 11 answers
  4. Complete the statement to describe the expression abc + defThe expression consists of _____ terms, and each term contains_____
    1. answers icon 5 answers
more similar questions