Jamie27 said:
6x^2+17x+12=___?
A) (6x+3)(x+4)
B) (6x+1)(x+12)
C) (2x+3)(3x-4)
D)(2x+3)(3x+4)
I came up with none of these answering the top equation? The closest I came was A?
Thank you!!!!
Jamie :roll:
Here's a method you can use to factor expressions of the form
ax<SUP>2</SUP> + bx + c
Step 1:
Multiply a * c (that is, the coefficient of the x<SUP>2</SUP> term and the constant term). In your problem, we multiply 6*12 to get 72.
Step 2: Look for two factors which produce the product ac, and which ADD UP to the coefficient of the middle term, b. In your problem, we need two factors of +72 which add up to +17 (the coefficient of the middle term). 9*8 is 72, and 9 + 8 is 17, so the numbers we want are 9 and 8.
Step 3: Use the numbers you found in step 2 to rewrite the middle term. For your problem, we'll use 9x + 8x instead of the middle term 17x:
6x<SUP>2</SUP> + 9x + 8x + 12
Step 4: Factor by grouping. Group the first two terms together, and the last two terms together:
6x<SUP>2</SUP> + 9x + 8x + 12
Remove the greatest common factor from each pair of terms:
3x(2x + 3) +
4(2x + 3)
Now, (2x + 3) is a common factor from both terms. Remove it:
(2x + 3)(3x + 4)
There's the factorization. This process works on any factorable (over the integers) quadratic polynomial and does not involve any trial-and-error.
I hope this helps you.