Factoring Quadratic Expressions
Factor Completely: 6x2 + 17x + 5
(3x+1)(2x+5)
Factor Completely: x2 + 9x + 18
(x+6)(x+3)
Factor completely: x2 + 6x + 9
(x+3)(x+3) or (x+3)2
*remember to use shortcuts
True or False: In an expression with any number of factors, if one is 0, the product will always be zero.
Correct Answer: True
*this is a definition we had copied down in our notebooks concerning the zero product property.
Find the x intercepts: (x-1)(3x-4)
x intercepts: (1,0) & (4/3,0)
Convert to standard form: (x+4)(x-9)
Standard Form: x2 - 5x - 36
Factor Completely: 4x2 + 4x + 1
(2x+1)2
Factor Completely: 9x2 - 100
(3x+10)(3x-10)
*remember to use shortcuts
Using the zero product property, find the x intercepts: (x-3)(x+4)
*please make sure to show work including the steps where this property was used.
x intercepts: (3,0) & (-4,0)
Find the x intercepts: (2x+1)(3x+2)
x intercepts: (-1/2,0) & (-2/3,0)
Factor Completely: 3n2 + 9n + 6
3(n+1)(n+2)
*In this quadratic, in order to factor completely you must pull out a factor, which in this case is 3.
Factor Completely: x2 + 4
Not Factorable
Please answer in your own words the question below:
What makes a quadratic expression a Perfect Square Trinominal?
- the squared term and solitary number must both be perfect squares (ex. x2 - 6x + 9)
- the second term must be double the square root of the last
*this information is from notes taken as a class in our notebooks if you need to refer back. Within this list is also how to use a shortcut method to solve these types of quadratics.
Using the zero product property, find the x intercepts: (2x-3)(4x-1)
*please make sure to show work including the steps where this property was used.
x intercepts: (3/2,0) & (1/4,0)
Find the x intercepts: x2 + 6x
x intercepts: (0,0) & (-6,0)
Factor Completely: 3 + 8k2 - 10k
(4x-3)(2x-1)
Factor completely: 5x2 - 45
5(x+3)(x-3)
*remember to factor out the 5
Factor Completely: 81y2 - 1
(9y-1)(9y+1)
*remember shortcuts
Using the zero product property, find the x intercepts: x2 - 6x - 16
*please make sure to show work including the steps where this property was used.
x intercepts: (8,0) & (-2,0)
Find the x and y intercepts: x2 - 2x - 8
x intercepts: (4,0) & (-2,0)
y intercept: (0,-8)
Convert to standard form: (6x-11)(2x+5)
Standard form: 12x2 + 8x - 55
Convert to standard form: (3x+2)2
Standard Form: 9x2 + 12x + 4
Please answer in your own words the question below:
What makes a quadratic expression a Difference of Squares?
Sample Answer:
- only two terms
- must be subtraction
- both terms are perfect squares
*this list is from notes taken as a class in our notebooks if you need to refer back. Within this list is also how to use a shortcut method to solve these types of quadratics.
Using the zero product property, find the x intercepts: 9x2 - 4
*please make sure to show work including the steps where this property was used.
x intercepts: (-2/3,0) & (2/3,0)
Find the x and y intercepts as well as the vertex: 2x2 + 8x + 6
x intercepts: (-3,0) (-1,0)
y intercept: (0,6)
vertex: (-2,-2)