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(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).
To factor the equation -6x^2 + 15x + 36, follow these steps:
Step 1: Look for the greatest common factor (GCF).
In this case, the GCF is 3. Divide each term by 3 to simplify the equation:
-2x^2 + 5x +12
Step 2: Look for a pattern.
The equation can be rewritten as:
(-2x^2 + 8x) + (x + 12)
Step 3: Group the terms.
Grouping these terms, we get:
2x(-x + 4) + 1(x + 12)
Step 4: Factor out the common factors.
Factor out -x + 4 from the first group and x + 12 from the second group:
(-x + 4)(2x + 1)
Step 5: Verify the factorization.
Multiply the factors (-x + 4)(2x + 1) to check if it equals the original expression -6x^2 + 15x + 36.
Therefore, the factored form of -6x^2 + 15x + 36 is (-x + 4)(2x + 1).