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When factoring the expression

4z2y +10x3y

you determine that the greatest common factor is:

(1 point)

14xy

2

LESSON FEEDBACK

O 10zy

O4zy

5 answers

To factor the expression \( 4z^2y + 10x^3y \), we need to determine the greatest common factor (GCF) of the two terms.

  1. Identify the coefficients:

    • The coefficients are 4 and 10. The GCF of 4 and 10 is 2.

  2. Identify the variables:

    • The first term has \( z^2 \) and \( y \).
    • The second term has \( x^3 \) and \( y \).
    • The common variable here is \( y \).

Combining these, the GCF of the expression \( 4z^2y + 10x^3y \) is:

\[ GCF = 2y \]

Thus, the greatest common factor (GCF) of the given expression is \( 2y \).

Based on the choices you provided, none of them correctly represent the GCF. However, if turned into options, it would be:

  • \( 2y \)
  • \( 4zy \)
  • \( 10zy \)
  • \( 14xy \)

The correct answer (GCF) is \( 2y \).

A: 14x5y9
B:2x2y4
C:10x3y5
D: 4xy

To determine the greatest common factor (GCF) among the expressions provided (A, B, C, D), we will analyze each expression based on their coefficients and variables.

A: \( 14x^5y^9 \)

  • Coefficient: 14
  • Variables: \( x^5 \), \( y^9 \)

B: \( 2x^2y^4 \)

  • Coefficient: 2
  • Variables: \( x^2 \), \( y^4 \)

C: \( 10x^3y^5 \)

  • Coefficient: 10
  • Variables: \( x^3 \), \( y^5 \)

D: \( 4xy \)

  • Coefficient: 4
  • Variables: \( x^1 \), \( y^1 \)

Step 1: Finding the Coefficient GCF

  • Coefficients: 14, 2, 10, 4
  • The GCF of 14, 2, 10, and 4 is 2.

Step 2: Finding the GCF of Each Variable

  • For \( x \):

    • From A: \( x^5 \)
    • From B: \( x^2 \)
    • From C: \( x^3 \)
    • From D: \( x^1 \)
    • GCF for \( x \) is \( x^1 = x \).

  • For \( y \):

    • From A: \( y^9 \)
    • From B: \( y^4 \)
    • From C: \( y^5 \)
    • From D: \( y^1 \)
    • GCF for \( y \) is \( y^1 = y \).

Step 3: Combine the Results

Now combine the GCFs:

  • Coefficient GCF: 2
  • \( x \) GCF: \( x \)
  • \( y \) GCF: \( y \)

So the overall GCF is: \[ GCF = 2xy \]

Conclusion

None of the options directly represent \( 2xy \). They represent different expressions from which \( 2xy \) could be factored out.

If you have further tasks or need specific help regarding any of these expressions, feel free to ask!

That's not a choice

Apologies for the confusion. Let's analyze the provided choices \(A\), \(B\), \(C\), and \(D\) and determine whether any of these are common factors of all the expressions.

Analyzing Choices:

  1. A: \(14x^5y^9\)
  2. B: \(2x^2y^4\)
  3. C: \(10x^3y^5\)
  4. D: \(4xy\)

Finding Common Factors

Let's see if we can find a common factor among all four options:

  • Common Coefficient: The coefficients of all terms include 14 (A), 2 (B), 10 (C), and 4 (D). The GCF of those coefficients is 2.

  • Common Variable \(x\):

    • The smallest power of \(x\) present in all terms:
      • A: \(x^5\)
      • B: \(x^2\)
      • C: \(x^3\)
      • D: \(x^1\)
    • The minimum is \(x^1\).

  • Common Variable \(y\):

    • The smallest power of \(y\):
      • A: \(y^9\)
      • B: \(y^4\)
      • C: \(y^5\)
      • D: \(y^1\)
    • The minimum is \(y^1\).

Common Factor

So, the common factor derived from all terms is: \[ 2xy \]

Choosing from the Options

Now, let’s see which of the given options includes this common factor:

  • Option A \(14x^5y^9\): This can be factored as \(2xy \cdot 7x^4y^8\) (contains \(2xy\)).
  • Option B \(2x^2y^4\): This can be factored as \(2xy \cdot x \cdot y^3\) (contains \(2xy\)).
  • Option C \(10x^3y^5\): This can be factored as \(2xy \cdot 5x^2y^4\) (contains \(2xy\)).
  • Option D \(4xy\): This can be factored as \(2xy \cdot 2\) (contains \(2xy\)).

Correct Response

Since they all can incorporate the common factor \(2xy\), any of the options \(A\), \(B\), \(C\), or \(D\) is a viable common factor.

If you are looking for the greatest common expression from the options that can encompasses \(2xy\), then any of the provided answers are valid as they are all factorizable by \(2xy\).

If you have a specific requirement or another angle you'd like to examine, let me know!