How do you factor #6x^2-5x-25#?
The answer is:
So factoring may seem hard but let take a look at what we could do.
So you first think of factors of the coefficient in front of
Now, if I choose
So let put it into the equation. But before we do that, we need a number that going to work for
Using the umbrella-XBOX method:
You should now have:
You must figure out what multiplies to get
1 - 150
2 - 75
3 - 50
5 - 30
6 - 25
10 - 15
15 - 10
25 - 6
30 - 5
50 - 3
75 - 2
150 - 1
Make a square box with four sections. Put the first term in the first box, the last term last, with the two middle terms in the two middle boxes. Then, do it like a Punnett square:
Here's how I've arranged mine, left to right: BB is
The next Bb is -15x. The maternal B is 3x, so 3x has to multiply by something to become -15x. -15x/3x = -5 , so the paternal b will be -5.
Therefore, maternal B is 3x, maternal b is 5, paternal B is 2x, and paternal b is -5, which is written as:
(3x + 5) = 0
(2x - 5) = 0
Solve like a one-step equation and you get:
SOURCE for PUNNETT SQUARE DIAGRAM:
(3x + 5)(2x - 5)
Use the new AC Method (Socratic Search)
Proceeding. Find the factor numbers of y', then, divide them by
a = 6. Find 2 numbers, that have opposite signs (ac < 0), knowing their sum (b = -5) and their product (ac = - 150).
They are: 10 and - 15.
The factor numbers of y are:
Note. This method avoids the lengthy factoring by grouping, and the solving of the 2 binomials.