Question

10 points! How do I factor 8x^2-26x+15

Answer 1

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 two 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 both 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.

Answer 2

(2x - 5)(4x - 3)

The AC method, also known as splitting the middle, can be shown like this:

8x^2 - 26x + 15

Check factors of 120.

1 * 120

-1 * -120

2 * 60

-2 * -60

3 * 40

-3 * -40

5 * 24

-5 * -24

6 * 20

-6 * -20 (these factors, when added together, are equal to the middle term, and thus splitting the middle term is possible.)

Split the middle term.

8x^2 - 6x - 20x + 15

Group in terms of 2.

(8x^2 - 6x) - (20x + 15)

Factor each binomial.

2x(4x - 3) - 5(4x - 3)

Rearrange the terms.

(2x - 5)(4x - 3)