Factor 8x^2 - 22x - 21 with steps shown?

Answer 1

Hi,

I' m going to explain factoring the way that I teach it, which is probably different from what you've done. Try to follow the steps. This method will work on any trinomial.

8x² - 22x - 21 Look for a GCF None this time. If there was one, factor it out. Then temporarily start both parentheses with the first number and variable.
(8x.......)(8x..........) First sign goes in first parentheses.
(8x..-....)(8x..........) Product of signs goes in 2nd parentheses.
(8x..-....)(8x...+.....) <== plus is because neg x neg = positive

Now multiply your first and third numbers together. Ignore their signs - you've already done them. 8 x 21 = 168. So, out to the side list pairs of factors of 168.

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

Now you want to pick which factors go in your parentheses, using these rules:

If the signs you put on your parentheses are the SAME, find the factors that ADD up to the middle number in the problem.
If the signs you put on your parentheses are the DIFFERENT, find the factors that SUBTRACT to the middle number in the problem. (Note you look at signs in the parentheses, not in the problem.)

(8x..-....)(8x...+.....) Your signs are different, so you want to subtract factors to get 22. Those factors are 6 and 28.
When you put the numbers in the parentheses, the bigger number is pushy - it always goes first. So your factors now are:
(8x..-..28)(8x.+.6)

Now you have to reduce either or both parentheses by dividing each parentheses' terms by the largest possible divisor. In our problem, the first parentheses is divisible by 4 and the second parentheses is divisible by 2.

(8x..-..28)(8x.+.6)
-------------.---------
.......4............2

This reduces to your final factors of

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

I know that's probably a different pattern for factoring, but it works on every trinomial - no more trial and error!

I hope that helps!! :-)

Answer 2

By showing the complete steps you would get as follows:
8x^2 - 22x -21
(4x - 7)(2x +3)
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At this point you need to equate both ( ) to 0 giving you:
(4x - 7) = 0; and (2x + 3) = 0
-----
After simplifying the equation you will get: 4x = 7 and 2x = -3
-----
By solving for x you will then have: x = 7/4 and x = -3/2
-----
Once you simplify the equations you will end up with x values of x = 1.75 and x = - 1.5.
-----
I hope this helps and good luck!

Answer 3

8x² - 22x - 21=
d = -22² - 4*8*-21
d = 484 + 672
d = 1156

x = (22 +/- 34) : 16
x' = 7/2
x" = 3/4
So,
Factor =
(2x - 7)(4x -3)
><

Answer 4

Delta = b^2 - 4ac
Delta = 22^2 -4(8)(-21)
Delta = 484 + 672
Delta = 1156

x1 = (-b + √Delta)/2a
x1 = (22 + √1156)2(8)
x1 = (22 + 34)/16
x1 = 56/16
x1= 7/2

x2 = (-b - √delta)/2a
x2 = (22 √1156)/2(8)
x2 = (22 - 34)/16
x2 = -12/16
x2 = -3/4

x = {7/2, - 3/4}

Answer 5

First try factors of 8x² as 4x and 2x:-
(4x-----?).(2x -----?)
Now have to replace ? with factors of 21 that combine with 4x and 2x to give - 22x:-
(4x-----3).(2x----7)
Applying appropriate signs gives:-
(4x + 3).(2x - 7)
Check
4x X 2x = 8x²
3 X - 7 = = - 21
-28x + 6x = - 22x

Answer 6

Ok, you need to think about factors of 8 & 21 first(1,2,4,8) & (1,3,7,21). Then which factors of 8 & 21 when you multiply the factors & then add answer together would give you the middle term. (2,4 & 3,7); We need to figure out in which order would give us the 22.
(2x-7)(4x+3){

Answer 7

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

you can use quadratic equation to find roots

-3/4 first root
7/2 sencond root

ax+b=0

since 4 and 2 are multiples of 8

try a=4

4x+b=0 b must be equal to 3

(4x+3) first term
(2x-7) must be second term if you multiply them together

Answer 8

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

Answer 9

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

Steps:_
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