i need help factorising this number. 8x squared -22x - 21.I am unable to split the middle term?

Answer 1

8x² - 22x - 21 = 0

find the sum of the middle term

Multiply the first term 8 times the last term 21 equals 168 and factor..

factors of 168 = 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84 168

- 28 and 6 satisfy the sum of the middle term

insert - 28x and + 6x into the equation

8x² - 22x - 21

8x² - 28x + 6x - 21

4x(2x - 7) + 3(2x - 7)

(4x + 3)(2x - 7)

- - - - - - - - - - - - - -s-

Answer 2

This is a guess and check method. Look at all the factors of the first and last terms. For 8 you have 8 and 1, or 4 and 2. For 21, there is 21 and 1, 7and 3. Use a T table and place the chosen pair of factors of 8 at the top of each column where you would normally place x and y. Say you choose 2x and 4x. Then below each of those you place your guess of the factors of 21, like so:
2x 4x
3 7
7 3
Now cross multiply, 2x times 7 = 14x, and 4x times 3 = 12x,. 12x and 14x can not get you the -22x by adding or subtracting. So draw line through the 3 and 7 and try the next pair. 2x times 3 = 6x and 4x times 7 = 28x. You can get -22x by 6x - 28x, so this tells you to place the negative on the 7 (which gave you the -28x). So now your binomial terms are lined up in columns. (2x-7)(4x+3).
Side note: if either of those had not worked you make a new T table using the 8x and 1x, and using all the factors of 21 again!
Hope this isn't too confusing, it becomes really quick and easy with a little practice!

Answer 3

=8x² -28x +6x -21
=4x(2x-7) +3(2x-7)
=(4x+3)(2x-7)

For roots Use formula.
[-b ± √(b² - 4ac)] / 2a

[-b ± √(b² - 4ac)] / 2a
[-(-22) ± √(-22² - 4(8)(-21)] / 2(8)
[22 ± √(484 + 672] / 16
[22 ± √1156] / 16
[22 ± 34] / 16

56/ 16 (or) -12/ 16

x = 3∙5 or x = -0∙75

At this point you can work the numbers back to get the factors.
x = 3∙5 or x = -0∙75
x - 3∙5 = 0 or x + 0∙75 = 0
(x - 3∙5)(x + 0∙75) = 0
At this point you can work the numbers back to get the original equation.
x² -2∙75 -2∙625 = 0
x² -2 3/4 -2 625/1000 = 0
x² -2 3/4 -2 25/40 = 0
x² -2 3/4 -2 5/8 = 0
x² -11/4 -21/8 = 0
8x² -88/4 -21 = 0
8x² -22 -21 = 0

Answer 4

Is there such as a word as factorising? I think the word is "factoring." Just asking, no offense. =)

Anyway, the factored form of the expression is:

(4x+3)(2x-7)

When solving for the middle term you come up with -28x +6x so you end up with -22x.

Hope that helps.

=)

Answer 5

8x^2 - 22x - 21
8*21 = 4*7 * 2*3 = 28 * 6, 28-6=22

(4x-+3)(2x -7)

Answer 6

When you are not able split the middle term ,clue is that find the roots using the formula -b+-Root of b^2-4ac divided by 2a and then try

Ans: (4x+3)(2x-7)

Answer 7

Roots are 7/2 and -3/4
thus (2x - 7)(4x +3) is the factorization required.

Answer 8

=8x^2-28x+6x-21
=4x(2x-7) +3(2x-7)
=(4x+3)(2x-7)

Answer 9

(4x+3)(2x-7)
Please give me best answer thanks!