Can someone point me in the right direction..i dont understand this
2007-07-22 05:40:11 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
15x - 22x - 5 - 0
The middle term is - 22x
Find the sum of the middle term
Multiply the first term 15 times the last term 5 equals 75 and factor
factors of 75
1 x 75
3 x 25. . .←. .use these factors
5 x 15
+ 3 and - 25 satisfy the sum of the middle term
insert + 3x and - 25x into the equation
15x² - 22x - 5 = 0
15x² + 3x - 25x - 5 = 0
Group factor
(15x² + 3x) - (25x - 5) = 0
3x(5x + 1) - 5(5x + 1) = 0
(3x - 5)(5x - 1) = 0
- - - - - - - - -s-
2007-07-22 07:48:21 · answer #1 · answered by SAMUEL D 7 · 0⤊ 0⤋
-22x = -25x + 3x
So:
15x^2 - 22x -5 = 15x^2 - 25x + 3x - 5
= 3*5x^2 - 25x + 3x - 5*1 . Now you have to guess:
= (3x - 5)*(5x + 1)
You see that the -25 came from the (-5)*(5)
This whole approach is not quite straightforward: You have to make some assumptions (that, for example, that only integers are involved) and you look at the coefficient of x^2 and the constant term to see how they could be factored to make the middle term come out properly.
To be honest, it's a question of "cut & try".
2007-07-22 05:55:31 · answer #2 · answered by ? 6 · 0⤊ 0⤋
15x^2 - 22x - 5
Rewriting the middle term as a sum of two terms is what is known as the "ac method"; it involves multiplying a and c, to get b. That is, for a quadratic expression
ax^2 + bx + c
ac = 15(-5) = -75
Now, find two factors of -75 which add up to -22. The two factors are -25 and +3. That's what we split the middle term, -22x, into.
15x^2 - 25x + 3x - 5
Now, factor the first two terms and the last two terms.
5x(3x - 5) + (3x - 5)
Which we can now group, as we have a common factor of (3x - 5).
(3x - 5) (5x + 1)
***
The general steps of the "ac method" goes as follows:
1) Calculate ac. Call it V.
2) Find two factors of V which add up to b.
3) Split the middle term as the factors of V.
4) Factor by grouping.
2007-07-22 05:51:57 · answer #3 · answered by Puggy 7 · 2⤊ 0⤋
i'll be honost with you i did it backwards i factored completely then figured out the sum of 2 terms
(3x-5)(5x+1)
then i figured out sum of two terms is -25x+3x
2007-07-22 05:48:03 · answer #4 · answered by sexy joker 6 · 0⤊ 0⤋
15x^2 + 25x - 3x -5
(15x^2 + 25x) - (3x + 5)
5x(3x + 5) - (3x + 5)
(5x - 1)(3x + 5)
Its called the ac method
2007-07-22 05:46:31 · answer #5 · answered by Anonymous · 0⤊ 0⤋
(15x^2-25x) + (3x-5)
5x(3x-5) + 1(3x-5)
(5x+1)(3x-5)
2007-07-22 05:53:16 · answer #6 · answered by D J 3 · 0⤊ 0⤋