Factor a crazy trinomial

TL;DR

Learn how to factor polynomials with multiple variables by identifying common factors and using the distributive property.

Transcript

we are going to factor this out we have 3x squared y square minus 23 XY to a third power plus 30 y to a fourth power as usual we'll see if it is any common factor that we can factor out first let's do Claddagh numbers we have three twenty three and thirty can we think about any common numbers that goes into these numbers no right and you see that f... Read More

Key Insights

• 🧑‍🏭 Factoring polynomials involves identifying common factors and using the distributive property.
• 🧑‍🏭 The polynomial 3x^2y^2 - 23xy^3 + 30y^4 can be factored by first factoring out y^2.
• 💁 The factored form of the polynomial is (3x - 5y)(x - 6y).

Questions & Answers

Q: What is the first step in factoring the given polynomial?

The first step is to identify a common factor, which in this case is y^2.

Q: How does factoring out y^2 affect the other terms in the polynomial?

Factoring out y^2 results in (3x^2 - 23xy + 30y^2), where the exponent of y in each term decreases by 2.

Q: How can the polynomial be further factored?

The polynomial can be factored using the distributive property as (3x - 5y)(x - 6y).

Q: Why is the combination of -5y and -6y the correct choice?

The combination of -5y and -6y is the correct choice because they multiply to give -30y^2, which matches the last term in the polynomial. Additionally, their coefficients (-5 and -6) add up to -11xy, matching the middle term.

Summary & Key Takeaways

• The content explains how to factor the polynomial 3x^2y^2 - 23xy^3 + 30y^4 by identifying common factors.

• After factoring out a common factor of y^2, the polynomial is rewritten as (3x^2 - 23xy + 30y^2).

• The polynomial can be fully factored as (3x - 5y)(x - 6y).