What are the steps to factoring problems such as 5d*squared*+6d-8?Please help!?

Question

I am a freshman in high school who has lost her notes! EEP!

Please,some thing that will work for most problems. I also do not want the answe r to this. I just want to know the steps that will help me find out the answer on my own.

Answer 1

well first, you start off with (5d ??)(d ??) because the only factors that multiply into 5 is 5 and 1. since the 8 is a negative because of the subtraction sign it means one side has a + and the other has a -. now you gotta figure out the factors for 8 which is 1x8 or 4x2. after that, you need to figure out which of the two numbers to put into the right place into order for it to add up to 6d. in this case, it would (5d - 4)(d + 2). using the FOIL method 5d times 2 into 10d and -4 times d is -4d and 10d - 4d is 6d.

Answer 2

5d^2 +6d -8
There is only one way to get 5d^2 and that is 5d times d
So you know that your two factors have to look like this:
(5d + ?)(d + ?)
Now look at -8. You can get this by +1*-8 or -2 *4 or -1*8 or 2*-4
So you need to figure which combination wil produce a middle term +6d
So just try them until you find a cobo that works
(5d+2)(d-4) This is no good because it gives a middle term of 2d -20d = -18d. So let's reverse them and get:
(5d-4)(d+2) This gives a middle term of -4d +10d = +6d. Great!!
That's what we wanted. To get the middle term you multiply the two inner terms together (in this case -4 and d) and add it to the result of mutiplying the tw outer terms (in this case 5d and 2).

In general if you have ax^2 + bx +c to factor you should check b^2-4ac and see what number you get. In the example we just performed a=5, b= 6 and c = -8, so
b^2 - 4ac = 6^2 -4(5)(-8) = 36+160 = 196 = 14^2 This tells you that you'll be able to factor the equation.
the roots of the equation will be [-b +/- sqrt(b^-4ac)]/2a
So you'll get [-6 +/- sqrt(14^2)]/2*5
= -6/10 +/- 14/10 = -2 or + 8/10 =4/5
So if x=-2, then (x+2) must be one of the factors.
Similarly if x= 4/5),then x -4/5 must be a factor which can be written as (5x-4)/5. Do you see how the 5x-4 is the same as the 5d-4 and the x+2 is the same as the d+2?

Answer 3

Sometimes it can be hard to find the two linear factors of a quadratic polynomial - a trial and error process. If you get stuck, use the quadratic formula. Set your polynomial equal to zero and solve it:

5d^2+6d-8 = 0

d = (-b +/- sqrt(b^2-4ac))/2a

Here a = 5, b = 6, and c = -8:

d = (-6 +/- sqrt(6^2-4*5*(-8))) / 2*5
= (-6 +/- sqrt(196))/10
= either (-6+14)/10 or (-6-14)/10
= either 8/10 or -20/10
= 4/5 or -2.

If the roots of ax^2+bx+c=0 are r and s, then its factors are a(x-r)(x-s).

Therefore, your factorization is:

5(x-4/5)(x+2) = (5x-4)(x+2)

Hope this helps.

Answer 4

first break up the first term and set up the parentheses:
(5d ) (d )

looking at the last term, which is -8, figure out the factors of this number, which are (-4,+2), (-2, +4), (-1,+8), (-8, +1)

then you look at the middle term, which is +6d. looking at the factors for -8, which ones, when the terms are all multiplied out, add up to +6d?

only (-4, +2) works.

so (5d-4) (d+2)

Answer 5

Find all the factors of the coeficients of the squared term and the constant term.
In this case the only prime factor of the squared term are 1 and 5
the factors of the constant term are (2 and 4) and (1 and 8)

The only possible factors of the formula are as follows
(d+1)*(5d-8)=5d*d -3d -8
(5d+1)*(d-8)=5d*d-39d-8
(d+2)*(5d-4)=5d*d+6d-8
(5d+2)*(d-4)=5d*d-18d-8
(d-1)*(5d+8)=5d*d+3d-8
(5d-1)*(d+8)=5d*d+39d-8
(d-2)*(5d+4)=5d*d-6d-8
(5d-2)*(d+4)=5d*d+18d-8

The answer is therefore (d+2)*(5d-4)=5d*d+6d-8