Make a box
Write the factors of the first term.
Write the factors of the last term.
Multiply on the diagonal and add to see if you get the middle term of the trinomial. If so, you’re done!
Difference of Squares
When factoring using a difference of squares, look for the following three things:
only 2 terms
minus sign between them
both terms must be perfect squares
If all 3 of the above are true, write two
( ), one with a + sign and one with a – sign : ( + ) ( - ).
1. a2 – 16
2. x2 – 25
3. 4y2 – 16
4. 9y2 – 25
5. 3r2 – 81
6. 2a2 + 16
Perfect Square Trinomials
When factoring using perfect square trinomials, look for the following three things:
last term must be positive
first and last terms must be perfect squares
If all three of the above are true, write one ( )2 using the sign of the middle term.
1. a2 – 8a + 16
2. x2 + 10x + 25
3. 4y2 + 16y + 16
4. 9y2 + 30y + 25
5. 3r2 – 18r + 27
6. 2a2 + 8a - 8
Now that we’ve learned all the types of factoring, we need to remember to use them all.
Whenever it says to factor, you must break down the expression into the smallest possible
Let’s review all the ways to factor.
Types of Factoring
Look for GCF first.
Count the number of terms:
4 terms – factor by grouping
3 terms -
look for perfect square trinomial
if not, try diamond or box
2 terms -
look for difference of squares
If any ( ) still has an exponent of 2 or more, see if you can factor again.
Solving Equations by Factoring
We know that an equation must be solved for the unknown.