Answer:
(3x - 2) and (x - 1)
Explanation:
The first step in factoring a polynomial equation in the form Ax² + Bx + C is to find the factors for the product of Coefficient A and Constant C whose sum is equal to the value of Coefficient B. This may sound difficult but it will make sense in practice.
To start, let's establish the terms of the equation.
The equation in Ax² + Bx + C form is 3x² - 5x + 2.
Coefficient A = 3
Coefficient B = -5
Constant C = 2
Next, we find the product of Coefficient A and Constant C, meaning we multiply the two together:
3 x 2 = 6
Now, we find list factors of 6, to find which two factors that when added together (this is the meaning of sum) would equal -5. I like to list them as factor pairs, and make sure to include the negative factors just in case:
1, 6; 2, 3; -1, -6; -2, -3
-2 x (-3) = -6 | -2 + (-3) = -5
We now substitute both factors, -2 and -3, into the original equation in place of Coefficient B.
3x² - 5x + 2 becomes 3x² - 2x - 3x + 2, or 3x² - 3x - 2x + 2
With this new equation, we separate the sets of terms into binomials and factor out their greatest common factors (GCFs). Again, this may sound more difficult than it is.
3x² - 3x - 2x + 2
(3x² - 3x) + (-2x + 2)
The GCF of 3x² and -3x is 3x. We divide each term of that first binomial by 3x.
The GCF of -2x and 2 is -2. We divide each term of that second binomial by -2.
3x(x - 1) - 2(x - 1) is what we are left with when the GCF are factored out.
If the binomials within the parentheses match, then you have found your factors for the original equation! These factors are the binomial within the parentheses and the binomial formed by the GCFs that were factored out.
So the factors of 3x² - 5x + 2 are (3x - 2) and (x - 1) or (3x - 2)(x - 1).
I hope this explanation helped!