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Van Goodman
Mathematics
8 December, 01:32
What is are the steps to factoring - x^2 + 6x - 9
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Eifel
8 December, 01:56
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Step-by-step explanation:
-x^2 + 6x - 9
The first step is to find the coefficient of x^2 (i. e. the num in front of x^2) = - 1
The constant is - 9
Therefore, the product of the equation = - 1 x - 9 = + 9
Sum of the equation = the coefficient of x = + 6
Then, we look for two factors (numbers) whose product = + 9, and sum = + 6
What of + 3 and + 3?
+3 + 3 = + 6
+3 x + 3 = + 9
Therefore, + 3 and + 3 are the factors of the equation.
We then substitute the sum of the equation (+6x) with these factors.
So, we have,
-x^2 + 3x + 3x - 9
We then pair the equation and equate to Zero
(-x^2 + 3x) (+3x - 9) = 0
Common factor in the first pair is - x and + 3 in the second.
-x (x - 3) + 3 (x - 3) = 0
At this stage, same factor must be in the bracket (i. e. x-3)
So, we now have,
(-x + 3) (x-3) = 0
We equate each to zero
-x + 3 = 0 and x-3=0
-x = - 3. and x = + 3
x = + 3 and x = + 3
Therefore, x = + 3 and + 3
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