100 points no links they don't work for me :) plz help to the best of your ability 3. Use the FOIL method to multiply binomials.
Part I: When multiplying binomials, the FOIL method helps you to organize the multiplication of each term of the first binomial by each term of the second. Fill in each blank with the word used to show how the binomials' terms are multiplied. (2 points: 0.5 point each)

F

O

I

L

Part II: Using the FOIL method, multiply the terms in the binomials below. Show your work in the blanks provided. Then, add any like terms and write the polynomial in standard form in the space provided. Show your work. (8 points: 2 points each)
A. (3x + 7)(2x – 5) B. (x2 + 2x)(5x2 – 3x)

+ + +
+ + +





C. (5x + 4)(5x – 4) D. (x2 – 7)(x2 – 4)

+ + +
+ + +




4. Use the distributive property to multiply the trinomial by the binomial.
Circle the first term in the trinomial, multiply it by each term in the binomial, and place each result in the blank spaces provided. Repeat this process for the second and third terms of the trinomial until all of the spaces are filled in. Finally, in the space provided beneath the blanks, simplify the expression by combining like terms and arranging the terms from highest to lowest order. Show your work. (4 points)

(3x2 – 2x + 7)(x2 + 2x)
+ + + + +

5. Use the vertical method to multiply two trinomials.
Step 1: Multiply the top trinomial by the last term in the bottom trinomial. Place each result in the blank spaces provided. (2 points)

Step 2: Multiply the top trinomial by the middle term in the bottom trinomial. Place each result in the blank spaces provided. (2 points)

Step 3: Multiply the top trinomial by the first term in the bottom trinomial. Place each result in the blank spaces provided. (2 points)

Step 4: Add the three partial products to find the final answer. Place the result at the bottom. (1 point)

6. Sabrina is making an open box from a piece of cardboard that has a width of 12 inches and a length of 18 inches. She'll form the box by making cuts at the corners and folding up the sides. If she wants the box to have a volume of 224 in3, how long should she make the cuts?

Part I: Each dimension (width, length, and height) of the finished box can be represented by a polynomial expression. If the height is x inches, what is the length in terms of x? (2 points)
Height = x
Width = 12 – 2x
Length =
Part II: The formula for volume is v = l • w • h. Use the polynomial expressions from Part I to write an equation to represent the volume of the box. Simplify on the right side by multiplying the polynomials and writing the answer in descending order. Show your work.
HINT: First multiply the binomials representing length and width. Next, multiply the resulting trinomial by the expression representing height. (3 points)
v =

Part III: The length of each cut at the corners is represented by x. To make a box, x must fall in a certain range of values. For example, x cannot be 15 because that would make the flap longer than the width of the box. Identify one reasonable value of x. Why did you choose that value? (2 points)

Part IV: Use the polynomial equation you wrote in Part II to find the volume of the box for each value of x. Show your work. (5 points)
x v
0

1

2

3 216
4

5

6 0
Part V: Based on your table, what x-value creates a box with a volume of 224 in3? (1 point)

Part VI: Using the polynomials from Part I and the value of x from Part V, what are the dimensions of Sabrina's completed box? (3 points)
Width =

Length =

Height =