1. TRINOMIALS
ax2 + bx + c

2. As stated earlier there are two versions of the trinomial method – a short cut method that can be used in certain situations and a longer, more drawn out method that can be used in all situations.
We have already learned about the short cut method. The more drawn out method works for all factorable trinomials. Because they take more steps to complete, it is better to use this method when the short cut method can’t be used. This happens with trinomials of the form: ax2 + bx + c, where a  1.
Factors of 72:
Example 1: 3x2 + 17x + 24 1 72 2 36
The first step is to multiply and ‘a’ term by the ‘c’ term and find the factors of ‘ac’.
In this example: 3  24 = 72 3 24 4 18 6 12 8 9

3. After finding the factors of 72, we must choose the factors that bring about a sum of the ‘b’ term.
In this example: b = 17
Factors of 72: 1 72 2 36 3 24 4 18 6 12 8 9
Factors of 72: 1 72 2 36
SUM = 17 3 24 4 18
Instead of selecting the chosen factors and using them as part of the binomial factors of the answer, they must be used to expand the trinomial expression into a four-termed expression. 6 12 8 9 {
3x2 + 17x + 24
3x2 + 17x + 24
At the point when the trinomial becomes a 4-termed polynomial, we can use the grouping method to continue factoring.
= 3x2 + 8x + 9x + 24
= 3x2 + 8x + 9x + 24
= 3x2 + 8x + 9x + 24
= x(3x + 8) + 3(3x + 8)
= x(3x + 8) + 3(3x + 8)
= (3x + 8) (x + 3)

4. { { Example 2: 8x2 + 11x - 10 a  c = 8  -10 Factors of -80:
+80
= 8x2 - 5x + 16x - 10
= 8x2 - 5x + 16x - 10 -2
+40
= 8x2 - 5x + 16x - 10
SUM = +11 -4
+20
= x(8x – 5) + 2(8x – 5)
= x(8x – 5) + 2(8x – 5) -5
+16 -5
+16
= (8x – 5) (x + 2) -8
+10
Example 3: 4x2 - 17x - 15
a  c = 4  -15 {
Factors of -60:
4x2 - 17x - 15 +1
-60
= 4x2 + 3x - 20x - 15 +2
-30
= 4x2 + 3x - 20x - 15 +3
-20 +3
-20
SUM = -17
= x(4x + 3) – 5(4x + 3)
= x(4x + 3) – 5(4x + 3) +4
-15 +5
-12
= (4x + 3) (x – 5) +6
-10

5. { { Example 4: 18x2 - 33xy + 5y2 a  c = 18  5 Factors of 90:-1
-90
= 18x2 - 3xy - 30xy + 5y2 -2
-45
= 18x2 - 3xy - 30xy + 5y2 -3
-30 -3
-30
SUM = -33
= 3x(6x – y) – 5y(6x – y)
= 3x(6x – y) – 5y(6x – y) -5
-18
= (6x – y) (3x – 5y) -6
-15 -9
-10
Example 5: 4c2 – 13c - 12 {
Factors of -48:
4c2 – 13c - 12 +1
-48
= 4c2 + 3c – 16c - 12 +2
-24
= 4c2 + 3c – 16c - 12 +3
-16 +3
-16
SUM = -13
= c(4c + 3) – 4(4c + 3)
= c(4c + 3) – 4(4c + 3) +4
-12
= (4c + 3) (c – 4) +6 -8