Factor: 18x^2-33x+9
Use the quadratic formula
and that will give you the answer
or, note that you have
3(6x^2-11x+3)
that will factor into
(6x-?)(x-?) or (3x-?)(2x-?)
where the two ? are either 1 or 3
a little thought will provide the answer:
3(3x-1)(2x-3)
To factor the given quadratic equation 18x^2 - 33x + 9, you can use the factoring method. Here's how to do it step by step:
Step 1: Check if you can factor out a common factor from all the terms.
In this case, all the terms have a common factor of 3. So, factor out 3 from each term:
3(6x^2 - 11x + 3)
Step 2: Look for two numbers that multiply to give the product of the coefficient of x^2 term (6) and the constant term (3), which is 18.
The numbers that multiply to give 18 are 6 and 3.
Step 3: Split the middle term (-11x) using the two numbers found in Step 2.
Write the split middle term (-11x) as (-6x - 5x), using the numbers 6 and 5.
3(6x^2 - 6x - 5x + 3)
Step 4: Group the terms and factor out the greatest common factor from each group:
3(x(6x - 6) - 1(6x - 6))
Step 5: Notice that we now have a common binomial factor, (6x - 6), in both groups. Factor it out:
3((x - 1)(6x - 6))
Step 6: Simplify further if possible.
Factor out 6 from (6x - 6):
3(6(x - 1)(x - 1))
Step 7: Final result.
The factored form of the quadratic equation 18x^2 - 33x + 9 is 3 * 6 * (x - 1)(x - 1).
Simplifying further, we get 18(x - 1)(x - 1).