I need to factor 8x^2 + 6x - 5 I do not know how to do this and I need to show each step of factoring out the GCF before I go to the next step, can anyone please help with this I am so lost on this
Thanks a great deal
2007-05-29 01:34:07 · 7 answers · asked by delphiniums 1 in Science & Mathematics ➔ Mathematics
8x² + 6x - 5 = 0
The middle term is + 6x
Find the sum of the middle term
multiply the first term 8 times the last term 5 equals 40 and factor
Factors of 40
1 x 40
2 x 20
4 x 10. . .<=. .use these factors
8 x 5
- 4 and + 10 satisfy the sum of the middle term
insert - 4x and + 10x into the equation
8x² + 6x - 5 = 0
Group factor
8x² - 4x + 10x - 5 = 0
4x(2x - 1) + 5(2x - 1) = 0
(4x + 5)(2x - 1) = 0
- - - - - - - - -
Roots
4x + 5 = 0
4x + 5 - 5 = 0 - 5
4x = - 5
4x / 4 = - 5 / 4
x = - 5/4
- - - - - - - - -
Roots
2x - 1 = 0
2x - 1 + 1 = 0 + `1
2x = 1
2x / 2 = 1 / 2
x = 1/2
- - - - - - - - -s-
2007-05-29 02:01:48 · answer #1 · answered by SAMUEL D 7 · 1⤊ 0⤋
8x^2 + 6x - 5
= (2x - 1)(4x + 5).
Factoring is largely trial and error.
You need to find two numbers which multiply together to give
-5. Those have to be 1 and -5 or -1 and 5.
You then consider how can the 8 from the 8x^2 be factored?
8:1 or 4:2 are the only possibilities.
As the coefficient of x is fairly small, this suggests 4:2 is a better bet than 8:1.
It also suggests putting the 4 where it will multiply by 1 and the 2 where it will multiply by 5, rather than the other way round.
If you get the right coefficient for x term but with the wrong sign, then the + and - in the two factors need to be switched.
2007-05-29 08:47:17 · answer #2 · answered by Anonymous · 0⤊ 0⤋
8x^2 + 6x - 5 =
8( x^2 + 6/8 x - 5/8) =
8( x^2 + 6/8x + (3/8)^2 - (3/8)^2 - 5/8) =
8( (x + 3/8)^2 - (9/64 + 40/64) =
8((x + 3/8)^2 - 49/64) =
8(x + 3/8 - 7/8)(x + 3/8 + 7/8) =
8(x - 1/2)(x + 5/2)
2007-05-29 08:57:01 · answer #3 · answered by Anonymous · 0⤊ 2⤋
8x squared + 6x -5 becomes (4x+5)*(2x-1)
written out it is 8x^2+10x-4x-5 simplified
to 8x^2+6x-5
2007-05-29 08:43:56 · answer #4 · answered by jonboy2five 4 · 0⤊ 2⤋
8x^2 + 6x - 5
=(2x-1)(4x+5)
2007-05-29 08:40:39 · answer #5 · answered by iyiem 2 · 0⤊ 2⤋
iyiem have you really helped this person?
As you can see, he/she has a number of factoring questions and he/ she is not able to solve as is evident by his/her repeated question.
We all know that you can solve it iyiem, now
he/she needs to know how to solve problems without any help, especially easy ones like this.
2007-05-29 08:48:23 · answer #6 · answered by Anonymous · 1⤊ 0⤋
last term is easy. huh?
( ___+/- 5)(___+/-1)
now how many ways can you make 8?
8x1
4x2
2x4
1x8
try each one!
2007-05-29 08:43:05 · answer #7 · answered by mikedotcom 5 · 2⤊ 0⤋