Need help with Polynomials As soon As possible. Thank you!

Question

1. The visual model below shows the multiplication of two binomials. Which two binomials are being multiplied?

2. The visual model below shows a trinomial. Which trinomial is shown?

3. Explain why the two visual models above are equal.

4. Create a visual model for the expression x(x + 1) using a paint program or by drawing on paper and inserting a photo of your work.

5. Use your visual model to explain why x(x + 1) = x² + x.

Answer 1

These first two questions are both basically asking you to come up with different equations for the area of the entire rectangle. Notice that the blue square has side lengths x, the yellow rectangles have side lengths x and 1, and the orange squares have sides of length 1.

1. The first way to find the area is to multiply the sides of the rectangle. The bottom side of the rectangle is: x+1+1+1=x+3. The right side is x + 1. Each of these sides is a binomial so we have A = (x + 3)(x+1)
2. The second way to find the area is to add up all the areas of the interior shapes. we have one x² area, four x areas and three 1 areas, so the equation adding these up is A = x² + 4x + 3

And we can verify they are equal by using FOIL:

A = (x + 3)*(x + 1)

= x² + x + 3x + 3

= x² + 4x + 3

so they are equal. The other questions should use some similar thinking.