Answer:
Yes, your answer is correct.
Step-by-step explanation:
A quadratic is usually represented as Ax^2+Bx+C.
Given quadratic is 8x^2-26x+15, so A=8, B=-26, C=15.
To factor a quadratic, one of the most used is what you term as the AC method.
This works as follows:
Step 1:
calculate the product AC=A*C=8*15=120
Step 2:
Find <em>two</em> factors of AC m and n such that
m*n = AC = 120
m+n = B = -26
Since the sum is negative, AND product is positive, we have <em>both</em> m and n negative!
You can list ALL the factors of 120 and try them in pairs:
{1,2,3,4,6,8,10,12,15,20,30,40,60,120}
Try the middle pair, -10*-12 = 120, but -10+(-12) = -22.
If the (absolute value of) the sum is too small, then go outwards.
{1,2,3,4,6,8,10,12,15,20,30,40,60,120}
Next pair to try is -8*-15=120. and -8+(-15) = -23, which is still too small.
Now try next pair:
{1,2,3,4,6,8,10,12,15,20,30,40,60,120}
Here, we have -6*-20 = 120, and
-6+(-20) = -26 =B, so we have found the necessary factors.
Step 3: Determine the coefficients of x in the individual factors by grouping
Write out the original expression as a sum of two binomials.
The first binomial is the x^2 term plus one of the factors (-6x) we found,we write
8x^2-6x
The second binomial is the other factor we found (-20x), added to the constant term 15, we write
-20x+15
Factor each binomial, and put together on one line
2x(4x-3) -5(4x-3)
We note that there is (4x-3) as a common factor, so factor that out again to get
(2x-5)(4x-3)
which is the final answer for the factoring problem.
