Rewrite this expression as the product of its greatest common factor and a polynomia 20y- 10ry + 15a?y?

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Factorization of a Polynomial Expression**

**Question 3:** Rewrite this expression as the product of its greatest common factor and a polynomial:

\[ 20y^6 - 10xy^3 + 15x^2y^2 \]

**Solution:**

1. **Identify the Greatest Common Factor (GCF):**

   - The coefficients of the terms are 20, -10, and 15. The GCF of 20, -10, and 15 is 5.
   - Next, look at the variables. The common factor for \( y \) is \( y^2 \) as it is the lowest power of \( y \) present in all terms.

   Therefore, the GCF of the given polynomial is \( 5y^2 \).

2. **Factor out the GCF from the polynomial:**
   
   \[ 20y^6 - 10xy^3 + 15x^2y^2 = 5y^2(4y^4 - 2xy + 3x^2) \]

Thus, the polynomial expression \( 20y^6 - 10xy^3 + 15x^2y^2 \) can be written as the product of its greatest common factor \( 5y^2 \) and the polynomial \( 4y^4 - 2xy + 3x^2 \).

Final Factored Form:
\[ 20y^6 - 10xy^3 + 15x^2y^2 = 5y^2(4y^4 - 2xy + 3x^2) \]
Transcribed Image Text:**Factorization of a Polynomial Expression** **Question 3:** Rewrite this expression as the product of its greatest common factor and a polynomial: \[ 20y^6 - 10xy^3 + 15x^2y^2 \] **Solution:** 1. **Identify the Greatest Common Factor (GCF):** - The coefficients of the terms are 20, -10, and 15. The GCF of 20, -10, and 15 is 5. - Next, look at the variables. The common factor for \( y \) is \( y^2 \) as it is the lowest power of \( y \) present in all terms. Therefore, the GCF of the given polynomial is \( 5y^2 \). 2. **Factor out the GCF from the polynomial:** \[ 20y^6 - 10xy^3 + 15x^2y^2 = 5y^2(4y^4 - 2xy + 3x^2) \] Thus, the polynomial expression \( 20y^6 - 10xy^3 + 15x^2y^2 \) can be written as the product of its greatest common factor \( 5y^2 \) and the polynomial \( 4y^4 - 2xy + 3x^2 \). Final Factored Form: \[ 20y^6 - 10xy^3 + 15x^2y^2 = 5y^2(4y^4 - 2xy + 3x^2) \]
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