Question
Factor the given polynomial by finding the greatest common monomial factor (or the negative of the gr \[ 21 x y^{2}+21 x^{3} y \] Answer
Ask by Warner Wade. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The factored form of the polynomial is \( 21xy(y + x²) \).
Solution
To factor the polynomial 21xy² + 21x³y, follow these steps:
1. Identify the common monomial factor in both terms. Both terms have a 21, an x, and a y.
2. Factor out the 21xy from each term:
21xy² = 21xy · y
21x³y = 21xy · x²
3. Write the expression as:
21xy(y + x²)
So the factored form is 21xy(y + x²).
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Simplify this solution Bonus Knowledge
To factor the polynomial \(21xy^2 + 21x^3y\), let's first identify the greatest common monomial factor. Both terms share a coefficient of 21 and the variables \(xy\). Thus, the GCF is \(21xy\). Now, we can factor it out from the polynomial: \[ 21xy^2 + 21x^3y = 21xy(y + x^2) \] So the factored form is \(21xy(y + x^2)\).
