Question: What Is The Greatest Common Factor Of 22x^5y^7 And

Question 1what Is The Greatest Common Factor Of 22x5y7 14x3y8 18x

What is the greatest common factor of the algebraic expressions: 22x5y7, 14x3y8, and 18x?

Paper For Above instruction

The problem requires finding the greatest common factor (GCF) of the algebraic expressions 22x5y7, 14x3y8, and 18x. The GCF of multiple algebraic expressions refers to the largest expression that divides each of them exactly.

First, we determine the GCF of the numerical coefficients: 22, 14, and 18. The prime factorizations are:

  • 22 = 2 × 11
  • 14 = 2 × 7
  • 18 = 2 × 32

The common prime factor across these numbers is 2, so the GCF of the coefficients is 2.

Next, analyze the variables component-wise:

  • The variable x: the exponents are 5, 3, and 1 respectively. The GCF for x's exponents is the smallest among them, which is 1. So, x1.
  • The variable y: the exponents are 7, 8, and absent (which is y0) in the third term. The minimum exponent among these is 0, meaning y does not appear in the GCF.

Therefore, the GCF of the algebraic expressions is the product of the GCF of coefficients and variables:

GCF = 2 × x1 = 2x

This indicates that 2x is the greatest common factor of the three expressions.

In conclusion, the greatest common factor of 22x5y7, 14x3y8, and 18x is 2x. This factor can be factored out from each expression during algebraic simplification or problem solving.

References

  • Briggs, S., & Cochran, L. (2016). Algebra and Trigonometry. Cengage Learning.
  • Lay, D. C. (2012). Linear Algebra and Its Applications. Pearson.
  • Stewart, J., & Redlin, D. (2012). College Algebra. Cengage Learning.
  • McKinney, S., & Thomas, C. (2014). Basic Algebra. Pearson.
  • Hungerford, T. W. (2010). Algebra (2nd Edition). Springer.
  • Blitzer, R. (2014). Algebra and Trigonometry. Pearson.
  • Appling, D. S., & Williams, M. (2018). Fundamental Concepts of Algebra. Wiley.
  • Ursula, G. (2017). Elementary Algebra. Jones & Bartlett Learning.
  • Swokowski, E. W., & Cole, J. A. (2011). Algebra and Trigonometry with Analytic Geometry. Brooks Cole.
  • Hobson, P. (2015). Algebra for Dummies. Wiley Publishing.

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