Polynoms and it's mishaps.

SmellyMan · 2012-01-15 10:03:56

I was doing some exercises and I stumbled upon this problem:

For which numbers a and b is this correct:

(x+a)(3x-2) = 3x²+x+b

So I try to get rid of everything I don't need.

3x²-2x+3ax-2a = 3x²+x+b

So, if I want the polynoms to be correct I have to get coefficient and the base number to be the same.

-2x+3ax = x
and
b=-2a

-2x+3ax = x
-2x-x = -3ax /divide by x

-2-1 = -3a and it comes to a = 1.

I put a in the base and I get b = -2

Am I doing this correctly? And I'd also love a correction if I did something wrong.

Regards!

bobbym · 2012-01-15 12:41:39

Hi SmellyMan;

Yes, you got the right answer! But you should do it like this:

3x²-2x+3ax-2a = 3x²+x+b

You use only the coefficients and not any x because you are looking for a coefficient, what the value of x is does not count here.

Now when you solve those you will get a = 1 and b = -2.

Also I need to mention one more thing. You should never, ever divide any equation by a variable like you did with x. Not unless it is stated somewhere that x does not equal 0. Here it is okay because x can not equal 0, so everything worked out fine. Remember in some equations x might be equal to 0 and division by 0 is a not allowed.

SmellyMan · 2012-01-16 02:45:59

Thanks for replying.

3x²-2x+3ax-2a = 3x²+x+b

Also, another question, you pointed out that I should just take the coefficient's.

And you wrote 3a-2=1

Wouldn't it be correct if it were 3a-2a=1 ?

And thanks for the 'tip'. I guess I haven't been paying attention to such details at the moment of solving. Will keep that in mind for later!

Thanks a bunch!

bobbym · 2012-01-16 02:48:41

Hi;

Wouldn't it be correct if it were 3a-2a=1

The 3a is a coefficient of x and the -2a is a coefficient of x^0, you can not combine them.

SmellyMan · 2012-01-16 04:18:26

bobbym wrote:

Hi;
Wouldn't it be correct if it were 3a-2a=1
The 3a is a coefficient of x and the -2a is a coefficient of x^0, you can not combine them.

I see.

So for example if I had

3x^2+5ax+3x+2 and

x^2+2x+1

It would be 5a+3 = 2 ?

Using this as an example.

bobbym · 2012-01-16 10:28:30

Hi;

Yes, that is correct!. This is called equating coefficients. You always match up the coefficients of like powers.

SmellyMan · 2012-01-18 03:45:03

bobbym wrote:

Hi;
Yes, that is correct!. This is called equating coefficients. You always match up the coefficients of like powers.

Thank you Bobby, I appreciate all the help you've given me!

And if my teacher would use this simple sentences maybe I'd understand it the first time she said it . Well, if I learn, it's worth it!

Thanks again, you've helped me out a bunch!

bobbym · 2012-01-18 03:52:45

Hi SmellyMan;

And if my teacher would use this simple sentences maybe I'd understand it the first time she said it

The disease is called jargonitis. Lots of mathematicians have caught it from those topologists, set theorists and logicians. There is currently no known cure.

anonimnystefy · 2012-01-18 08:43:45

and from applied mathematicians and physicists too!

Math Is Fun Forum

#1 2012-01-15 10:03:56

Polynoms and it's mishaps.

#2 2012-01-15 12:41:39

Re: Polynoms and it's mishaps.

#3 2012-01-16 02:45:59

Re: Polynoms and it's mishaps.

#4 2012-01-16 02:48:41

Re: Polynoms and it's mishaps.

#5 2012-01-16 04:18:26

Re: Polynoms and it's mishaps.

#6 2012-01-16 10:28:30

Re: Polynoms and it's mishaps.

#7 2012-01-18 03:45:03

Re: Polynoms and it's mishaps.

#8 2012-01-18 03:52:45

Re: Polynoms and it's mishaps.

#9 2012-01-18 08:43:45

Re: Polynoms and it's mishaps.

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