Monic Factoring and Difference of Squares
What is the factored form of:
x^2 - 100
(x+10)(x-10)
What is a term made from? (3 things)
Coefficient, Variable, and Exponent
What does i = ?
sqrt(-1)
How does a solution relate to a factor? Partial credit: Use (x - 67)
A factor helps you quickly find the solution. In that given factor, x=67 is the solution.
What is the factored form of the following:
3x^2 -8x -35
(3x + 7) (x - 5)
What is the factored form of:
x^2 + 7x + 6
(x+6)(x+1)
What is a quadratic?
An x squared polynomial!
What does
i^4 =
1
How many solutions does a quadratic have?
Two
Kaleb uses the quadratic formula below. What are his solutions?
(-6+- sqrt (36-32))/2
-4 and -2
What is the factored form of:
x^2 + 5x + 6
(x+2)(x+3)
(3x+7)(2x-3)=6x^2 +5x -21
What is (3x+7) called?
A FACTOR
(6+7i)+(6+7i)
12+14i
If a quadratic has no REAL solutions, what does that mean about its solutions?
The quadratic has 2 complex solutions
Caleb uses the quadratic formula below. What are his solutions?
(9+- sqrt (81-32))/2
(9 +- sqrt(59))/2
What is the factored form of:
25x^2 -9
(5x-3)(5x+3)
What are at least two more names for a solution?
Roots, x-intercepts, and/or zeroes
(6+7i)*(6-7i)
85
How many solutions does a linear polynomial have?
Kaleb uses the quadratic formula below. What are his solutions?
(8 +- sqrt (64-32))/2
4 +- 4sqrt2
What is the factored form of:
x^2 - 10x + 25
(x-5)(x-5)
What is a complex conjugate? For partial points, what is the complex conjugate of
6 + 7i
A complex conjugate is the same as a specific complex number, except the imaginary part has a different sign.
Example: 6 + 7i has complex conjugate 6 - 7i
(6+7i)*(6+7i)
-13 + 84i
What does the Quadratic Formula do?
Finds the solutions to any quadratic, regardless of complex or real solutions
What are the solutions to the following polynomial?
x^2 + 6x + 10
-3 +- i