how do you factor completely..
18x^2+3x-3?
3(6x^2-x-1)
3(2x-1)(3x+1) check that.
(2x+1)(9x-3)
(2x+1)(9x-3) one more step
(2x+1)(3)(3x-1)
To factor the given expression completely, 18x^2 + 3x - 3, follow these steps:
Step 1: Verify if there is a common factor
Check if there is a common factor among all three terms. In this case, there is no common factor other than 1.
Step 2: Multiply the coefficient of the x^2 term by the constant term
Multiply the coefficient of the x^2 term (18) by the constant term (-3). In this case, 18 * (-3) = -54.
Step 3: Find two numbers that multiply to give the result from Step 2 and add up to the coefficient of the x term
Find two numbers that multiply to give -54 and add up to the coefficient of the x term (3). In this case, the two numbers are 6 and -9, because 6 * (-9) = -54 and 6 + (-9) = -3.
Step 4: Rewrite the expression using the two numbers from Step 3
Rewrite the expression using the two numbers found in Step 3. Split the middle term (3x) into two terms, using 6x and -9x. The expression becomes:
18x^2 + 6x - 9x - 3
Step 5: Group the terms and factor by grouping
Group the terms together, taking the common factor out of each group:
(18x^2 + 6x) + (-9x - 3)
Factor out the greatest common factor from each group:
6x(3x + 1) - 3(3x + 1)
Step 6: Factor out the common binomial factor
Now, there is a common binomial factor, (3x + 1), which can be factored out:
(3x + 1)(6x - 3)
Therefore, the completely factored expression is (3x + 1)(6x - 3).