Math Homework Help?

Question

I'm in Algebra 2 and this is what the problem is:

Solve by Factoring.

2x^2-9x+4=0

please tell me how to do this because I am so lost, thanks!

Answer 1

Okay, so solving by factoring means the opposite of the FOIL method (first terms, outside terms, inside terms, last terms). So what you need to do is come up with two equations that multiply together to make that quadratic. This is useful because it is much quicker than using the quadratic method for simpler equations

Because you have the x-squared term, that means you need an x in each of the two equations. Because it's 2x, one of them needs to be x, and the other 2x. So...

(2x plus or minus something) x (x plus or minus something)

The second term in the equation has to multiply together to make the number without an x coefficient. In this case, 4. We have two choices, 2 and 2, or 4 and 1. We decide which we need because added together (and multiplied by the 2x) they have to equal -9x. In that case, you can see that it has to be 4 and 1.

So....

(2x plus or minus 1) (x plus or minus 4)

You decide whether it's plus or minus by looking at the original equation. The last term is positive, so either both must be plus or both must be minus. The second term is negative, so that means they both have to be minus. So...

(2x -1)(x-4)

Then you set each of these equal to 0, and solve.

2x-1 =0
2x = 1
x = 1/2

x-4 = 0
x = 4

So the answers are 1/2 and 4

Answer 2

There's always trial and error. If you don't like that, there's a method that always works but can be complicated to explain in a forum like this. Let's give it a stab:

You know from the trinomial that the factors must be of the form

(ax - b)(cx - d)

i.e. minuses in both. You know that because the constant is positive but the linear term is negative - that's the only way to do it. Now: Multiply the leading coefficient (2) by the constant (4) to get 8. You're looking for factors of 8 that add to 9.

If the factors had had different signs:

(ax + b)(cx - d)

then you'd be looking for factors that multiply to the constant but DIFFER by the linear term.

In any event, with your problem: factors of 8 that add to 9, 8 and 1 are the obvious choice. Now split it up, and it doesn't really matter how you do that:

2x^2 - 9x + 4 =

2x^2 - 8x - x + 4

Now take them in pairs and factor out the common factors:

2x(x - 4) - (x - 4)

Note that we have two factors of (x - 4), so pull it out, and you're left with

(x - 4)(2x - 1) = 0

At this point, it's easy:

x = 4 or x = 1/2

Hope that wasn't too confusing. This process always works if the trinomial can be factored.

Answer 3

first u start off by setting up a pair of parentheses to accomodate your factors such as ( ) ( ) = 0
then u break u the first term 2x^2 u usually break up the exponent first by dividing by 2 so x squared would just b x like x^4 would b x^2 anyways we get ... (2x ) (x ) = 0
next u look at the last term 4 and think of its factors ... 1x4 ... 2x2 ... 4x1 which would b the same as 1x4 so we only have 2 :D 1x4 and 2x2 these are the numbers that are gonna accompany the lonely x's in the parentheses =P what u have to worry about is getting them to add up to the middle term which in this case is a 9 ... if ure not used to this step its always good to just try the factors till u get used to it and u can just do it in your head ... so trying the factor of 1x4 we get ... (2x 1)(x 4)
Next we have to work on the signage in these parentheses ... looking at the middle term we c that it is negative (-9) and the last term is positive (+4) in order to achieve a positive sign ont he last term the only 2 posible combinations for the parentheses are (+,+) or (-,-) and seeing as the middle term is negative we eliminate the (+,+) sooo
(2x-1)(x-4)= 0 As we FOIL (First Outer Inner Last) or Funny Face (cuz its supposed to look like a funny face ... dont ask lol) to check our answer we get ...
First ~ (2x)(x) = +2x^2
Outer ~ (2x)(-4) = -8x
Inner ~ (-1)(x) = -x
Last ~ (-1)(-4) = +4
Putting them all together we get ~ 2x^2-8x-x+4
We combine like terms (the x's)
2x^2-9x+4 which checks out as our starting equation meaning these are the correct factors and correct signs so we go back to our parentheses.... (2x-1)(x-4)= 0

We set each parenthese equal to zero and then solve
so ... 2x-1=0 and x-4=0
We solve for x and find that x = to 1/2 and 4 respectively and thats the answer = ) hope i was of some help and didnt confuse u more = S

Answer 4

I'm not sure how to tell you how but i'll tell u the answer and try to figure out how i got to that step ok?

(2x-1)(x-4)
It's multiplying,
*first you have to know that there is going to be a 2x and a xin. order for there to be a 2x^2
*then you find the signs, they are going to be negative because the 4 and the 9 are both negative
*finally, when you multiply through u need to get 9x so -4*2x=-8x
and -1*x =-1 , add those to get -9.

I hope that helped.

Answer 5

(2x-1)(x-4) is the answer