5. Dividing Polynomials
Sign In
Consider the given prism with a triangular base.
The volume of the prism is 10w3+23w2+5w−2, where its height is 2w+1 and the height of the triangular base is 5w−1. We will calculate the length of the base of the triangle. To do so, let's first find an expression for the area of the triangular base B by using the formula for the volume of a prism.V=10w3+23w2+5w−2, h=2w+1
LHS/2w+1=RHS/2w+1
Rearrange equation
2w10w3=5w2
Multiply term by divisor
Subtract down
2w18w2=9w
Multiply term by divisor
Subtract down
2w-4w=-2
Multiply term by divisor
Subtract down
B=5w2+9w−2, h=5w−1
LHS⋅2=RHS⋅2
Distribute 2
LHS/5w−1=RHS/5w−1
Rearrange equation
5w10w2=2w
Multiply term by divisor
Subtract down
5w20w=4
Multiply term by divisor
Subtract down
When we are doing long division by hand, it looks a bit different than how we have it in this solution. Here is how yours should look when you are writing it in your notebook. Let's start with the division of 10w3+23w2+5w−2 by 2w+1.
Let's now show how to divide 10w2+18w−4 by 5w−1 by hand.