Hello, my name is__________________________
ALGEBRA II: Polynomial Concept Problems and Solving Equations.
1. A carpenter hollowed out the interior of a block of wood as shown above (image on the left).
a) Express the volume of the original block as a polynomial in standard form.
b) Express the volume of the hollowed out block as a polynomial in standard form.
c) Write a polynomial for the wood remaining.
2. A metalworker wants to make an open box from a sheet of metal by cutting equal squares from each
corner as shown above (image on the right).
a) Write an expression for the length, width, and height of the open box.
b) Find the volume of the box as a polynomial P(x)
c) Graph. Find the max volume and the size of the square cut that gives this volume.
Hello, my name is____________________________
ALGEBRA II: Polynomial Concept Problems and Solving Equations.
1. A carpenter hollowed out the interior of a block of wood as shown above. (Image on the left)
a) Express the volume of the original block as a polynomial in standard form.
b) Express the volume of the hollowed out block as a polynomial in standard form.
c) Write a polynomial for the wood remaining.
2. A metalworker wants to make an open box from a sheet of metal by cutting equal squares from each
corner as shown above (image on the right).
a) Write an expression for the length, width, and height of the open box.
b) Find the volume of the box as a polynomial P(x)
c) Graph. Find the max volume and the size of the square cut that gives this volume.
Hello, my name is__________________________
3) The picture shows a rectangular region with one corner on the graph of y = -x2 + 2x + 4
Solving by graphing
a) Write a polynomial in standard form for the area A of the region
b) Find the area of the region for x = 2.5
Solve x3 + 3x2 = x + 3
Two ways: 1) Get everything same side. Find intersection with y = 0
2) Graph both sides separately and find where they hit each other. (where equal)
Sum of Cubes
a3 + b3
Difference of Cubes
Examples:
x3 + 8
a 3 + b3
x3 – 27
Problems to do: pg. 330, 1-5, 12, 13, 15, 16, 18, 48, and Luggage problem from yesterdays sheet.