Factoring Techniques

Question 1

The difference of 2 squares

Answer 1

When (a^2-b^2)

Equals the square root of a plus the square root of b, times the square root of a minus the square root of b

Question 2

Greatest common factor

Answer 2

Factor out the GCF

Question 3

Perfect square trinomial

Answer 3

When

The square root of ax^2
Times
The square root of c
Times 2
Equals bx

Of

F(x)=ax^2+bx+c

Question 4

Grouping when a>1

Answer 4

Multiply ax^2 times c

Factor that into two numbers that add together to make bx

Group the four terms into pairs and factor

Take the GCF to get two terms

Question 5

Square root method

Answer 5

When the linear term is missing
f(x)=x^2+c
The square root of x^2 equals +/- the square root of c

In vertex form
f(x)=a(x-h)^2+k
The square root of [a(x-h)^2] equals +/- the square root of k
Then add or subtract h from both sides

Question 6

Completing the square

Answer 6

When a=1 and best if bx is positive

Set y=0

Add or subtract c from both sides

Divide b by 2 and square the answer

Add that number to both sides

Now you have a perfect square trinomial on one side

Take the square root of both sides

Simplify for x

Remember +/- when taking square roots

Question 7

Completing the square when a>1

Answer 7

Make a=1 by taking the GCF

Complete the square

Divide both sides by taking the GCF times the number for c which you added to complete the square

Question 8

Quadratic formula

Answer 8

X is equal to

-b +/- the square root of (b^2-4ac)
Divided by
2a