6.3 Adding, Subtracting and Multiplying Polynomials Warm Up:
Multiply, add, or subtract the following polynomials
1.) 2( x − 5)
2.) − 4( x 2 − 5 x + 1)
3.) (3 x)(2 x)
4.) 7 m 2 − 12m 2
Add, Subtract or Multiply the following: 1.) (3 x 3 + 2 x 2 − x − 7) + ( x 3 − 10 x 2 + 8) =
2.) ( x + 2)(5 x 2 + 3 x − 1) =
3.) (2 x 2 + 3 x) − (3 x 2 + x − 4) =
4.) ( x 3 − 2 x + 1)( x 3 + x 2 − 5) = 5.) (2 x + 1)( x + 3)( x + 1)
6.) (2 x − 3)(2 x − 5)( x − 1)
7.) (6 x + y ) 2 =
8.) (3x − 5) =
3
6.3 Adding, Subtracting and Multiplying Polynomials In this lesson, you will design an open box out of grid paper that is 20 grids
by 18 grids. The box will be formed by making the square cuts shown in the
diagram and folding up the sides.
x
x
x
x
x
x
x
x
x
Volume of a Box = (Length)(Width)(Height)
x
Volume
1.) Which value of x maximizes the volume of the box?
2.) Are there other possible values of x that that could provide a larger volume?
3.) Provide the formula for the volume of the box in terms of x:
Volume of the box =
What is the range for this problem?
VOLUME 4.) Graph the function above on your graphing calculator. Sketch the part of
graph below that makes sense in the context of the problem.
500
What is the domain for this problem?
x
5.) Use your calculator to find the value of x that maximizes the volume of the box.
6.3 Adding, Subtracting and Multiplying Polynomials