Factoring Frenzy
Factor:
x^2+5x+6
What is (x+2)(x+3)?
What value of c would make this a perfect square trinomial:
x^2+10x+c
25
What is the name of this type of problem:
x^2-36
Difference of Squares
Which equation is in vertex form? Identify the vertex
a) (x+8)2+10
b) x2-16x+21
c) (x+11)(x+4)
a) (x+8)2+10 is in vertex form and the vertex is (-8, 10).
Which method would you use to solve
x^2+2x-8=0
Either will work, but factoring may be easier.
Factor and solve:
x^2-2x-10=-2
.
What is (x+2)(x-4)=0 and x=-2 and x=4
Solve by completing the square:
x^2+6x+9=0
(x+3)^2=0
and x=-3
What is the name of this type of problem:
x^2+12x+36
Perfect Square Trinomials
Identify the vertex:
y=(x-2)^2-5
Vertex is
(2,-5)
Is
2x^2+5x+9
factorable? Explain
No, there are no factors of 18 that add to 5.
Factor and Solve:
2 x^2+10x+3=3x
(2x+1)(x+3)=0
x=-1/2, 3
Solve by completing the square:
x^2-8x+6=0
x=4+-sqrt10approx7.16,0.84
Which of the following is not factorable? Why?
a) x2-16 b) x2-8x+16 c)x2+25 d) 100x2-81
c) is not factorable because it is sum of squares rather than differnece of squares. there are no factors of 25 that add to 0.
Solve and identify the vertex:
(x-1)^2+4=0
x=1+-2i Vertex: (1,4)
How many solutions are there? What kind of solutions are they?
(x+10)^2=12
There are 2 irrational solutions:
x=-10+-2sqrt3
What makes a trinomial prime (not factorable)?
There are no factors of c that add to b.
The solutions are most likely irrational or imaginary.
Solve by completing the square:
4x^2+8x+1=0
x=+-1/2
Explain the difference between perfect square trinomials and difference of squares.
PST has 3 terms and in factored form it is 2 of the same thing. Ex: x2-4x+4=(x-2)(x-2) or (x-2)2.
Difference of squares only has 2 terms. Factored form is almost the same but one is + and the other is -. Ex: x2-49=(x+7)(x-7)
Use the process of completing the square to find the vertex form and the vertex:
x^2-8x+10=0
(x-4)^2-6
(4, -6)
How many solutions are there? What kind of solutions are they?
x^2+16=0
There are 2 imaginary solutions:
+-4i
Factor and Solve:
4x^2-12x+7=x^2-2x
(x-1)(3x-7)=0
x=1, 7/3
Why do we find (b/2)2 and add it to both sides?
(b/2)2 is the value that wil turn x2+bx into a perfect square trinomial. If we add it to the left, we must add it to the right as well to preserve equality.
Name the problem type and factor:
9x^2-64
Difference of squares
(3x+8)(3x-8)
A student forgot the
+-
what happened to their answer?
They only found one solution when there should be 2.