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Complex Numbers
Equations in Standard Form
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Long Division
Word Problems
100
In the equation 5-2i, which number is the real number?
The 5
100
What can you get from standard form?
Standard form is helpful for determining the vertex, x, and y intercepts for quick graphing.
100
How do you classify a polynomial?
Classifying a polynomial depends on its degree, or highest power of "x" in the equation
100
Divide 3x^3 – 5x^2 + 10x – 3 by 3x + 1
x^2 - 2x + 4 + (-7)/(3x + 1)
100
A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.
The pool is 15 feet wide and 30 feet long (2x + 4)(x + 4) - (2x)(x) = 196 2x² + 8x + 4x + 16 - 2x² = 196 12x + 16 = 196 12x = 180 x = 15
200
Solve: (-6+5i)+(4-8i)
-2-3i
200
Write in standard form: f(x)=-x^2-6x+3
-(x+3)^2+12
200
Add (3y^5 − 2y + y^4 + 2y^3 + 5) and (2y^5 + 3y^3 + 2+ 7)
5y^5+y^4+5y^3-5y+7
200
Divide 2x^3 – 9x^2 + 15 by 2x – 5
x^2-2x-5+10/2x-5
200
The side of a cube is represented by x + 1. Find, in terms of x, the volume of the cube.
x³+3x²+3x+1cubic units Volume = length•width•height Volume = (x+1)(x+1)(x+1) = (x+1)(x²+2x+1)
300
Solve: (-2)-(6-2i)
-8+2i
300
Write in standard form: 3x^2+12x-22
3(x+2)^2-34
300
Subtract (3y^5 − 2y + y^4 + 2y^3 + 5) and (2y^5 + 3y^3 + 2+ 7)
2y^5+y^4-y^3-9y+3
300
Divide 4x^4 + 3x^3 + 2x + 1 by x^2 + x + 2
4x^2-x-7+11x+15/x^2+x+2
300
Write a variable expression for the area of a square whose side is x + 8.
x² + 16x + 64 square units Area = length • width Area = (x + 8)(x + 8) = x² + 8x + 8x + 64
400
What does i^50 equal?
-1 50/4=12r2 --->i^50=i^2=-1
400
Find the vertex of (x+1/2)^2-21/4
(-1/2, -21/4)
400
Multiply: 3x(x^2 – 9x + 2)
3x^3 – 27x^2 + 6x
400
Divide x^3-4x^2+2x+5/x-2
x^2-2x-2+1/x-2
400
Let an integer be represented by x. Find, in terms of x, the product of three consecutive integers starting with x.
x³ + 3x² + 2x Consecutive integers are integers that follow one after the other, such as 12, 13, 14. Algebraically, consecutive integers are represented as x, x+1, x+2. The product will be x(x+1)(x+2) = x³ + 3x² + 2x
500
Write in standard form: 5-2i/-4+i
-22/17+3i/17
500
Find the x and y intercepts for the equation (x+1/2)^2-21/4
X intercept-(-2.8,0) Y intercept- (0,5)
500
Multiply: 6y^6(–3y^3 + 3y^2 + y – 2)
–18y^9 + 18y^8 + 6y^7 – 12y^6
500
Divide 2x^3-4x+7x^2+7 by x^2+2x-1
2x+3+-8x+10/x^2+2x-1
500
Think of a number. Subtract 7. Multiply by 3. Add 30. Divide by 3. Subtract the original number. The result is always 3. Use polynomials to illustrate this number trick.
Think of a number x Subtract 7 x - 7 Multiply by 3 3(x - 7) = 3x - 21 Add 30 3x - 21 + 30 = 3x + 9 Divide by 3 (3x + 9)/3 = x + 3 Subtract original x + 3 - x = 3 No matter what number you start with, you always end up with 3.