Factor 3g squared - 7g +2

3g^2 - 7g + 2

(3g-?)(g-?)

The only factors of 2 are 1 and 2. So, how can you place them to get -7 in the middle?

X power 4 +x square + 1

To factor the quadratic expression 3g^2 - 7g + 2, we can follow these steps:

Step 1: Identify the coefficients of the quadratic terms.
Our quadratic expression is 3g^2 - 7g + 2.

Step 2: Multiply the coefficient of the quadratic term by the constant term.
In this case, the coefficient of the quadratic term is 3 and the constant term is 2. Multiplying them together gives us 3 * 2 = 6.

Step 3: Find two numbers that multiply to the result in Step 2 (6) and add up to the coefficient of the linear term (-7).
In our case, we need to find two numbers that multiply to 6 and add up to -7. These numbers are -6 and -1, since -6 * -1 = 6 and -6 + (-1) = -7.

Step 4: Rewrite the linear term using the two numbers obtained in Step 3.
The quadratic expression can be rewritten as 3g^2 - 6g - g + 2.

Step 5: Group the terms with a common factor.
In this case, we can group the first two terms (3g^2 - 6g) and the last two terms (-g + 2).

Step 6: Factor out the greatest common factor from each group.
From the first group (3g^2 - 6g), we can factor out a common factor of 3g, resulting in 3g(g - 2).
From the second group (-g + 2), there is no common factor to factor out.

Step 7: Combine the factored terms.
Now, we can combine the factored terms from step 6 to get the final factored form:
3g(g - 2) - 1(g - 2).

Step 8: Factor out the common binomial factor.
In this case, (g - 2) is a common factor that can be factored out. So, the final factored form is:
(g - 2)(3g - 1).

Therefore, the factored form of the quadratic expression 3g^2 - 7g + 2 is (g - 2)(3g - 1).