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Could someone please show me how to factor this using the x method

Could someone please show me how to factor this using the x method-example-1
User Cyclion
by
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2 Answers

5 votes

Answer:

(x + 2) (8x + 3)

Explanation:


8x^(2) +
19x + 6

= (x + 2) (8x + 3)

L = 3/a = 3/8

R = 16/a = 16/8 = 2

User Kader
by
7.5k points
5 votes

\ac/

L V R

/ \

/ b \

where letters have their usual meaning. Comparing 8x² + 19x + 6 to ax² + bx + c,

ac = 8*6 = 48

b = 19

Factors of ac or 48 :-

1 * 48

2 * 24

3 * 16

As the sum of 3 and 16 is 19(or b), our required pair is 3 and 16.

On the left side:

L = 3/a = 3/8

On the right side:

R = 16/a = 16/8 = 2

Therefore, factorized form is (x + 3/8)(x + 2) which can be written as (8x + 3)(x + 2).

How this method works:

Make a X with ac and b on the top and bottom of the X, where ac and b are taken from ax² + bx + c.

On the left side we have d/a and e/a. Basically d and e are those values that we get after solving the whole question.

Step1: find the pair(s) for which sum of factors of ac = b. Here it is 3 and 16.

Step2: put these values in place of d and e.

Step3: solve left anf right of X,

Left = d/a = 3/8

Right = e/a = 16/8 = 2

Step4: whatever you get, put that in (x+?)(x+?) in place of ?.

User Kaiyuan Xu
by
7.9k points

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