Question
rewrite the polynomial as a product of a monomial and a polynomial.
15x^3y^2 + 10x^2y - 20x^2y^3
15x^3y^2 + 10x^2y - 20x^2y^3
Answers
GPT-4o mini
To rewrite the polynomial \(15x^3y^2 + 10x^2y - 20x^2y^3\) as a product of a monomial and a polynomial, we start by factoring out the greatest common factor (GCF) of the terms.
1. Identify the GCF:
- For the coefficients \(15\), \(10\), and \(-20\), the GCF is \(5\).
- For the variable \(x\), the lowest power is \(x^2\).
- For the variable \(y\), the lowest power is \(y\).
Thus, the overall GCF is \(5x^2y\).
2. Factor out the GCF:
\[
15x^3y^2 + 10x^2y - 20x^2y^3 = 5x^2y(3xy + 2 - 4y^2)
\]
So, the polynomial rewritten as a product of a monomial and a polynomial is:
\[
5x^2y(3xy + 2 - 4y^2)
\]
1. Identify the GCF:
- For the coefficients \(15\), \(10\), and \(-20\), the GCF is \(5\).
- For the variable \(x\), the lowest power is \(x^2\).
- For the variable \(y\), the lowest power is \(y\).
Thus, the overall GCF is \(5x^2y\).
2. Factor out the GCF:
\[
15x^3y^2 + 10x^2y - 20x^2y^3 = 5x^2y(3xy + 2 - 4y^2)
\]
So, the polynomial rewritten as a product of a monomial and a polynomial is:
\[
5x^2y(3xy + 2 - 4y^2)
\]