Question

# For each problem below, perform the indicated operations. Leave your answers as polynomials in simplest form.

• 2x2+x-x2-8x-5

• 3x2-4x+7+x2-2x+5

• x3-2x2+x-4-3x2-x-5

2. Consider the product 3x(2x+4).

2.Draw an area model to represent this product.

Use your area model to help you write an equation with the product 3x(2x+4) on the left side f the equation and the equivalent polynomial on the right.

3.Consider the product of two binomials (x+3)(x+2).Draw an area model to represent this product.

3.Use your model to write an equation with the product of the two binomials on the left and the equivalent polynomial on the right.

4.Even though lengths and areas are not generally represented using negative numbers, a rectangular diagram can still be used to help you multiply any two binomials.

4.Draw a rectangular diagram for (x+3)(x-4).

4.Use the distributive property to multiply (x+3)(x-4). Show each step of your work.

5.Multiply each of the following binomials using the distributive property.

a(x+6)(x-7).

b(x-4)(x+4)

c(2x-1)(3x+4)

6.In Problem 6, each of the polynomials you obtained by multiplying the binomials is a quadratic trinomial in the form ax2+bx+c.

a. Describe what you notice about a (the lead coefficient of the trinomial) as it relates to the binomials in each case.

b. Describe what you notice about b as it relates to the binomials in each case.

c. Describe what you notice about c as it relates to the binomials in each case.

1. Use what you discovered in Problem 7 to convert these quadratic functions in factored form to standard form. Try to do the multiplication in your head and write only the final polynomial.

1. fx=x+3x+8

1. fx=x-6x-7

1. fx=x-8x+5

1. fx=x-45x+7

1. fx=3x-13x-1

1. Use the distributive property to find these products.

1. fx=3x-1x2-x-1

1. fx=2x+1x2-x+6