Factoring polynomials: common factor area model | Mathematics II | High School Math | Khan Academy

TL;DR

The length of a rectangle can be found by determining the greatest common monomial factor of the area, while the width can be derived by dividing the area by the length.

Transcript

• [Voiceover] The rectangle below has an area of 12x to the fourth plus 6x to the third plus 15x squared square meters. And we can see the area right over here and they broke it up; this green area is 12x to the fourth, this purple area is 6x to the third, this blue area is 15x squared. You add 'em all together, you get this entire rectangle which ... Read More

Key Insights

• 🧑‍🏭 The length of a rectangle can be found by identifying the greatest common monomial factor of the terms in its area equation.
• 🗂️ The width of a rectangle is obtained by dividing the area by the length.
• 🧑‍🏭 The greatest common factor of the coefficients in the area equation provides the coefficient of the length.
• ☺️ The highest power of x that is divisible by the powers of x in the terms represents the power of x in the length.

Questions & Answers

Q: How can the length of a rectangle be determined from its area?

The length of a rectangle can be found by identifying the greatest common monomial factor of the terms in the area equation. This factor represents the length.

Q: How can the width of a rectangle be calculated using the area and length?

To calculate the width of a rectangle, divide the area by the length. The resulting expression represents the width of the rectangle.

Q: What is the process for finding the greatest common monomial factor?

To find the greatest common monomial factor, examine the coefficients of the terms in the area equation. Determine the common factors and select the largest one. Then, consider the powers of x present in each term and find the highest power that is divisible by all the terms.

Q: How is the width of the rectangle derived from the area and length?

After determining the length, divide the area of the rectangle by the length. The resulting quotient represents the width of the rectangle.

Summary & Key Takeaways

• The provided content demonstrates how to find the length and width of a rectangle given its area, which is expressed as a polynomial equation.

• The greatest common monomial factor of the terms in the area equation represents the length of the rectangle.

• Dividing the area by the length gives the width of the rectangle.