gr.10 math!
posted by Saira on .
factor the equation: 6x^2+15x+36
please show me the steps in answering this problem.
thanksss..)

What are the factors of 1000

6x^2+15x+36 is an expression. An equation has an equal sign.
First take out common factors
3(2x²5x12)
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*43=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 (x4)(2x+3).
Check by expanding: 2x²8x+3x12=x²5x12
The final answer is 3(x4)(2x+3).