Factoring
Polynomials
Quadratics
Multi-Step Equations
Find the Roots
100
Factor:
(x6 - 100)
What is
(x3 + 10)(x3 - 10)
100
Combine like terms:
x2 + 2x2 + 3x + 2x
3x2 + 5x
100
The two methods that we have learned to solve a quadratic...
Factoring and using the quadratic formula
100
Solve for x:
x + 5 = 11
x = 6
100
What are the roots of the following quadratic?
0= (x + 2) (x + 5)
(-2, 0) and (-5, 0)
200
Factor:
x2 + 5x + 6
(x + 5)(x + 1)
200
3x2 - 6x2
-3x2
200
The roots of this parabola...
(-1, 0) and (3, 0)
200
2x + 6 = 14
x = 4
200
What are the roots of the following quadratic?
0= (x + 3) (x - 8)
(-3, 0) and (8, 0)
300
Factor:
x2 - 5x - 24
(x - 8)(x + 3)
300
Multiply
(x - 2) (x +3)
x2 + x - 6
300
Evaluate the x-coordinate of the vertex of the following quadratic:
x2 - 6x + 3
x = 3
300
2 (x + 1) = x + 6
x = 4
300
Find the roots:
y= x2 + 5x - 6
x = -6 , x = 1
(-6, 0) and (1, 0)
400
x2 - 25
(x - 5) (x + 5)
400
Which expression is the sum of
x2 + 2x - 5 and 2x2 + 3x - 5 ?
4x2 + 6x + 12
400
2 (x + 8) = 6(3x)
2x + 16 = 18x
-2x -2x
16 = 16x
x = 1
400
Evaluate the roots for the following quadratic:
0= x2 -7x +12
0= (x - 3)(x - 4)
Roots: (3, 0) and (4, 0)
500
2x2 - 24x + 72
2 (x2 - 12x + 36)
.... 2(x - 6)(x - 6)
500
Which expression is TWICE the sum of
x2 + x + 3 and x2 + 2x + 3 ?
4x2 + 6x + 12
500
What is the axis of symmetry of the following quadratic?
x2 + 20x -5
x = -10
500
Solve for x:
2(4x - 3) - 8 = 4 + 2x
x = 3
500
What are the roots of the following quadratic?
0 = x2 - 7x -8
(8, 0) and (-1, 0)