GCF Factoring of Trinomials
GCF Factoring
GCF FACTORING
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Factoring the GCF from expressions is a lot of fun!
You first want to check for a common GCF among all the terms. Then you have to factor out a common GCF. The GCF multiplied by the expression inside the parentheses is equal to the original expression.
GCF factoring
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After factoring the gcf, you have to put terms in the parentheses that multiply with the gcf to equal its corresponding term.
Factoring 2 terms
Factoring 2 terms (binomials)
One way is to factor out the GCF. All you would do is factor out the common GCF and then you would write the terms in the parentheses that multiply with the GCF to be the original terms of the expression. Then, you have to factor the expression in the parentheses and that gives you your answer.
Another way of factoring binomials is to use the difference of squares method. This is when a  b= (a +b)(a  b).
Factoring 3 terms
One way of factoring 3 terms is by splitting the middle method. First, you want to find the product of ac, that is your "magic number". When you find that number you try to find numbers that multiply to be that number and add up to be the middle term of the expression.
Once you get that, you substitute those two numbers in for that middle number. After that you factor by grouping. If the leading coefficient is 1 than it is a simple trinomial.To factor simple trinomials you have to check if the middle number is twice the product of the square roots of the 1st and last term.
Example of factoring three terms using the split the middle method.
Factoring 4 term polynomials
First you check if there is a common GCF among all the terms.
If there is a common GCF then you factor out the GCF
After that you factor by grouping.
Factor again.
Examples of 4 term polynomials that can be factored by grouping
5x+20x+10
GCF:5
5(1x+4x+2)
9x6x+12x
GCF:3x
3x(3x2+4)
2
Prime
You do not have to do any thing to the expression. It can not be factored because the terms have no common gcf with each other.
Therefore you leave it as it is.
FACTORING TRINOMIALS
If there was no common GCF among the terms you would have to factor by grouping two terms in the polynomial and another two terms. Then you would have to factor out the gcf from each group of terms. Then the you get the answer by writing down the common binomial and the left over binomial.
3
Some examples of this are,
4x+11x 7x+8
2x  11x +3
2
3
Examples of perfect square trinomials
9x+14x+16
=(3x+4)
1x10x+25
=(x5)
x+20x+100
=(x+10)
2
2
20x+11x3
1. 20*3= 60
2. 15+(4)= 11
3. 20x+15x4x3
4. 5x(4x+3) 1(4x+3)
5.(4x+3) (5x1)
2w
3
+
w
2

14w7
=w(2w+1) 7(2w+1)
=(w7) (2w+1)
8x+4x8x4x
=4x(2x+1x2x1)
=4x[x(2x+1)1(2x+1)]
2
2
Factoring binomials
1 . Factor out the GCF
12x9x
=3x(4x3)
2. Factor using the difference of squares
X 36
=(x+6) (x6)
2
2
Factoring perfect square trinomials
You can factor a perfect square trinomial into two binomial factors that are the same. The first and last terms can be written as the product of the two factors that are the same. The middle term is twice the product of the square root of the first and last term.
2
2
2
2
2
2
4
3
2
3
2
2
4x(
x
2
1)
(2x+1)
3
2
2
2
2
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