Question
Factor the given polynomial by finding the greatest common monomial factor (or the negative of \[ 2 x y^{2}+10 x y+11 x^{3} y \]
Ask by Bowman Frazier. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Factor out \(xy\) from the polynomial to get \(xy(2y + 10 + 11x^2)\).
Solution
Factor the expression \( 2xy^2+10xy+11x^3y \).
Factor the expression by following steps:
- step0: Factor:
\(2xy^{2}+10xy+11x^{3}y\)
- step1: Rewrite the expression:
\(xy\times 2y+xy\times 10+xy\times 11x^{2}\)
- step2: Factor the expression:
\(xy\left(2y+10+11x^{2}\right)\)
The greatest common monomial factor of the given polynomial \(2xy^2+10xy+11x^3y\) is \(xy\). Factoring out \(xy\) from the polynomial, we get \(xy(2y+10+11x^2)\).
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Simplify this solution The Deep Dive
To factor the polynomial \( 2xy^2 + 10xy + 11x^3y \), start by identifying the greatest common monomial factor among the terms. Here, you can see that each term contains at least one factor of \( xy \). Factoring out \( xy \), we get: \[ xy(2y + 10 + 11x^2) \] Now, let's simplify the expression inside the parentheses. The polynomial is now written as \( xy(11x^2 + 2y + 10) \). This gives a clearer expression of the original polynomial, showcasing the common factor neatly. Next, if you're interested in solving equations, this approach helps you systematically tackle polynomials in various forms. Remember to always look for common factors first!
