Adding & Multiplying Polynomials
What is a polynomial?
An algebraic expression in terms of variable x.
What are the factors of 4x^2+2x+6x^3?
2 and x
Solve for x: 3x+5=2
x=-1
Solve for x: x-2<3
x<5
What are the values of x: x^2-4=0
x=2,-2
What is combining similar terms?
Combining values with the same base (x) and the same power. We add them like adding regular numbers.
How do we factor x^2+6x+8?
Use x method, use x as factors of x^2, then find factors that multiply to 8 that add to middle term 6. Those numbers are 4 and 2 so factored form is
(x+4)(x+2)
y=mx+b
Solve for x: -2x-3>5
How do we complete the square for x^2+6x+2?
First, divide 6 by 2 and square it for our c term. When we do this, we get x^2+6x+9. We then subtract x^2+6x+2 from x^2+6x+9. It all cancels out to -7 (we need to subtract 7 from 9 to get our c value 2). x^2+6x+2= x^2+6x+9-7=(x+3)^2-7.
Final answer: (x+3)^2-7
What is the distributive property?
Multiplying a value outside of a parenthesis by all the terms in the parenthesis.
Example: 2(x+3)=2x+6
How do we find x when x^2+2x-3=0
Factor, then set the factored form equal to 0. Since at least one factor must equal 0, we set both to 0 and solve both equations for x.
F: (x-1)(x+3)=0, x-1=0, x+3=0, x=1 and x=3
In the equation of an Area of a circle, what is the input and what is the output? A=pi*r^2
Solve for x: |x|=5
x=5,-5
What do a, b, and c represent in quadratic equations?
The coefficients of x^2, x, and the constant respectively.
Simplify:(x^3+2x-1)+(2x^2-x^3)
2x^2+2x-1
When there are no apparent factors that multiply to last term in quadratic expression and to middle term, what methods do we use?
Quadratic Formula & Completing the Square
How do we make r the output and A the input in the equation of the area of a circle: A=pi*r^2?
r=sqrt(A/pi)
Solve for x: |x-2|-4=5
x=11, -7
How do we ensure that we know whether our equation is a perfect square by using the Quadratic formula?
Multiply: 2(x+2)(x-5)
2(x^2-3x-10)=2x^2-6x-20
Solve for x: x^4-5x^2+4=0
Then set x^2-4=0 and x^2-1=0
x^2=4, x^2=1, x=-2,2,-1,1 (4 answers)
Solve for y: 3(y-9)=5(x-7) and then describe the graph by identifying the y-intercept and slope.
y=(5x-8)/3 Slope=5/3, y-intercept=-8/3
Solve for x: 2|x+7|-5<6
-12.5<x<-1.5
Use quadratic formula to solve: 3x^2+5x-8. Is our solution real? How many are there?
x=(-5+11)/6 and (-5-11)/6. Yes, our solutions are real. There are 2 of them.