Posted by **Saira** on Saturday, September 19, 2009 at 2:08am.

factor the equation: -6x^2+15x+36

please show me the steps in answering this problem.

thanksss..)

- gr.10 mathh! -
**Joe**, Saturday, September 19, 2009 at 4:00am
What are the factors of 1000

- gr.10 mathh! -
**MathMate**, Saturday, September 19, 2009 at 7:44am
-6x^2+15x+36 is an expression. An equation has an equal sign.

First take out common factors

-3(2x²-5x-12)

Now concentrate on the part in parentheses.

Make a table of possible combinations of factors that multiply to the constant term (-12) and put them in the first two columns. For example, -1 and 12.

Multiply the first column by the coefficient of the term in x² (2) and add to the second column. Put the result in the third column (-1*2 + 12 = 10):

-1 12 10

Compare the third column with the coefficient of the term in x, i.e. -5. If they compare, you have found the factors: (x+A)(2x+B) where A and B are the numbers in the first and second columns.

Let's continue:

A B 2*A+B

#-1 12

12 -1 12*2+(-1)=23

#2 -6

4 -3 2*4-3=5 (Found, but wrong sign)

-4 3 2*(-4)+3=-5 (switched sign)

# Since we have already taken out all common factors, we do not have to check cases where B is even, which makes 2x+2k (k=integer).

The intermediate answer is (x-4)(2x+3).

Check by expanding: 2x²-8x+3x-12=x²-5x-12

The final answer is -3(x-4)(2x+3).

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