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Is there a GCF between all of the terms in the given expression? If so, you should factor that out first.
3(x-1)(x-4)
Let's start factoring by first identifying the greatest common factor. Then, we will rewrite the expression as a trinomial with a leading coefficient of one.
3( x^2-5x+4) Let's temporarily only focus on this trinomial, and we will bring back the GCF after factoring.
To factor a trinomial with a leading coefficient of one, think of the process as multiplying two binomials in reverse. Let's start by taking a look at the constant term. x^2-5x+4 In this case, we have 4. This is a positive number, so for the product of the constant terms in the factors to be positive, these constants must have the same sign (both positive or both negative.)
Factor Constants | Product of Constants |
---|---|
1 and 4 | 4 |
-1 and -4 | 4 |
2 and 2 | 4 |
-2 and -2 | 4 |
Next, let's consider the coefficient of the linear term. x^2-5x+4 For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, -5.
Factors | Sum of Factors |
---|---|
1 and 4 | 5 |
-1 and -4 | -5 |
2 and 2 | 4 |
-2 and -2 | -4 |