Solve in Factored Form
The solution to
(x+2)(x-1) = 0
is this.
What is x = -2 and x = 1
These are the solutions to the equation
x2 + 3x + 2 = 0
What are x = -2 and x = -1
These are the solutions to the equation
x2 + 1 = 5
What are x = 2 and x = -2
This is what happens when you square root (x + 2)2
You get x + 2
(the square and square root cancel out)
The a, b, and c of the equation
x2 + 3x + 2 = 0
are this.
What are a = 1 b= 3 and c = 2
The solution to
(4x+8)(x-5) = 0
is this.
What is x = -2 and x = 5
These are the solutions to the equation
x2 - 9x - 22 = 0
What are x = 11 and x = -2
These are the solutions to the equation
3x2 + 1 = 10
What are x = sqrt(3) and x = -sqrt(3)
These are the solutions to the equation
(x - 4)2 = 9
What are x = 7 and x = 1
The a, b, and c of the equation
3x2 - 4x + 1 = 3x - 4
are this.
What is a = 3 b = -7 and c = 5
The solution to
3x(2x-7) = 0
is this.
What is x = 0 and x = 7/2
Explain why it is important for us to factor equations before solving them.
Because we need to split our equations into two different parts. This allows us to find what makes each part equal to 0.
These are the solutions to the equation
2x2 - 3 = -51
What are x = 2i sqrt(6) and x = -2i sqrt(6)
These are the solutions to the equation
(x - 5)2 + 1 = 26
What are x = 10 and x = 0
This is the solution to the equation of
x2 + 5x + 2 = 0
What is -5 +- sqrt(17) / 2
The solution to
(4x-10)(10x+1) = 0
is this.
What is x = 10/4 (5/2 or 2.5) and x = -1/10 (-0.1)
These are the solutions to the equation
2x2 + 5x + 7 = 4
What are x = -1 and x = -3/2 (-1.5)
These are the solutions to the equation
x2 + 1 = 2x2 - 10
What are x = sqrt(11) and x = -sqrt(11)
These are the solutions to the equation
3(x - 9)2 = 81
What are x = 3sqrt(3) + 9 and x = -3sqrt(3) + 9
This is the solution to the quadratic equation of
3x2 - 5x + 1 = 4
What is 5 +- sqrt(61) / 6
Give an example of an equation that would have three solutions instead of two solutions in factored form.
Ex. (x+1)(x-2)(x+3) = 0
These are the solutions to the equation:
5x2 - 6x - 8 = 5x - 10
What are x = 1/5 (0.2) and x = 2
Explain why paired numbers in a factor tree "escape" the square root.
By definition, a square root is looking for two of the same number multiplied. Ex. sqrt(16) = 4 because 4*4 = 16. We are finding smaller perfect squares in the number and simplifying them out.
These are the solutions to the equation
6(x - 2)2 - 10 = -76
What are x = isqrt(11) + 2 and x = -isqrt(11) + 2
This is the solution to the quadratic equation of
2x2 - 7x + 12 = x2 + 2
What is x = 5 and x = 2