Using polynomial to represent the area of a box to factor out the GCF

The video tutorial explains factoring polynomials by relating it to finding the side lengths of a rectangle. The teacher introduces the concept of factoring out the greatest common factor (GCF) and uses a rectangle analogy to help students visualize the process. The tutorial guides students through identifying common factors and calculating the GCF, using 5X as an example. Finally, the teacher demonstrates how to express the polynomial in its factored form.

What is the relationship between multiplying two polynomials and the area of a rectangle?

• The product of two polynomials is unrelated to area.

• The product represents the volume of a cube.

• The product represents the perimeter of a rectangle.

• The product represents the area of a rectangle.

When breaking down the area of a rectangle into smaller sections, what are we trying to find?

• The height of the rectangle.

• The common side length.

• The color of the rectangle.

• The diagonal of the rectangle.

Which number can be used as a common factor for the numbers 55, 10, and 15?

• 3

• 5

• 10

• 15

What is the greatest common factor of the polynomial 5X^3 + 10X^2 - 15?

• 15

• 5X

• X

• 5

How would you express the polynomial 5X^3 + 10X^2 - 15 in its factored form?

• 5X^3 + 10X^2 - 15

• X(5X^2 + 10X - 15)

• 5(X^3 + 2X^2 - 3)

• 5X(X^2 + 2X - 3)