- x^2 + 9x -18
i didn't explain....i need to factor...but i don;t get when there is a negative in front of the x
sorry
thanks
-x^2 factors to ... -x and x
find two factors of -18, that can sum to 9 (with a little sign adjustment)
... 6 and 3 will work ... with one of them negative
(-x + 6) and (x - 3) will FOIL to ... - x^2 + 9x -18
You can always do this for this type of question:
- x^2 + 9x -18
= -(x^2 - 9x + 18)
= -(x-3)(x-6) , which should have been easy to see
Now you could write that as:
(3-x)(x-6) or (x-3)(6-x)
No problem! I can help you with factoring the quadratic expression -x^2 + 9x - 18. Factoring involves finding two binomials that, when multiplied, give you the original expression.
To factor a quadratic expression, follow these steps:
Step 1: Set the expression equal to zero by adding a "-x^2 + 9x - 18" to both sides of the equation. This will give you: -x^2 + 9x - 18 = 0.
Step 2: Find two numbers that multiply to give you the product of the coefficient of the x^2 term (which is -1) and the constant term (which is -18), and add up to give you the coefficient of the x term (which is 9). In this case, the numbers are -6 and 3 (-6 * 3 = -18, -6 + 3 = 9).
Step 3: Rewrite the middle term (9x) using the numbers from step 2. So, the expression becomes: -x^2 - 6x + 3x - 18.
Step 4: Group the terms and factor by grouping. In this case, we will group the first two terms and the last two terms:
(-x^2 - 6x) + (3x - 18).
Step 5: Factor out the greatest common factor from each group. In the first group, we can factor out an "x", and in the second group, we can factor out a "3":
x(-x - 6) + 3(x - 6).
Step 6: Notice that both terms have a common factor of "(x - 6)", so we can factor it out:
(x - 6)(-x + 3).
Thus, the factored form of -x^2 + 9x - 18 is (x - 6)(-x + 3).
Please let me know if you have any further questions!