Help: (x-3) is a factor of x^2-4x+c, find c?

[nukeman]

Homework Statement

If (x-3) is a factor of: x^2 - 4x + c, what is c?

Homework Equations

The Attempt at a Solution

I am really stuck here. When presented with these types of questions, what is the FIRST thing you look at/do ?

Thanks so much.

 

[Mark44]

Homework Statement

If (x-3) is a factor of: x^2 - 4x + c, what is c?

Homework Equations

The Attempt at a Solution

I am really stuck here. When presented with these types of questions, what is the FIRST thing you look at/do ?

Thanks so much.

There's a theorem that deals with this. If x - a is a factor of a polynomial f(x), then f(a) = 0.

Here's an example:
f(x) = x³ - x² - 5x - 3

As it happens, f(x) can be factored into (x - 3)(x² + 2x + 1).

This means that x - 3 is a factor of f(x). It also means that f(3) = 0. We can verify this by calculating f(3) = 3³ - 3² - 5(3) - 3 = 27 - 9 - 15 - 3 = 0.

 

[SammyS]

Homework Statement

If (x-3) is a factor of: x^2 - 4x + c, what is c?

Homework Equations

The Attempt at a Solution

I am really stuck here. When presented with these types of questions, what is the FIRST thing you look at/do ?

Thanks so much.

The first thing I ask, is what do you know about polynomials and factoring.

For this problem, "What is the remainder of (x² - 4x + c)÷(x-3), if (x-3) is a factor of x² - 4x + c ?"

 

[nukeman]

Holy crap, think I got it. Please let me know if correct?

If (x-3) is a factor of: x^2 - 4x + c, what is c?


(3)^2 - 4(3) + c

9 - 16 + c = 0

c = 7

? is that correct?

 

[LCKurtz]

Holy crap, think I got it. Please let me know if correct?

If (x-3) is a factor of: x^2 - 4x + c, what is c?(3)^2 - 4(3) + c

9 - 16 + c = 0

c = 7

? is that correct?

Do you really have to ask that? Is x-3 a factor of $x^2-4x+7$? If it is you are done, otherwise you might want to check your arithmetic.

 

[SammyS]

Holy crap, think I got it. Please let me know if correct?

If (x-3) is a factor of: x^2 - 4x + c, what is c?


(3)^2 - 4(3) + c

9 - 16 + c = 0

c = 7

? is that correct?

What is 4(3) ?

(It's not 16.)

 

[nukeman]

Oh, I wrote on my paper 4(4)

 

[nukeman]

So correct answer is:

c = +3

Umm... sorry if this is a dumb question, but the last 2 I did, C is always the same as what they are telling is a factor of.

So, this one I just did, they say (x+3) is a factor of... would c automatically be +3?

The answer turned out to be +3.

Can someone give me another simular example to try?

 

[SammyS]

So correct answer is:

c = +3

Umm... sorry if this is a dumb question, but the last 2 I did, C is always the same as what they are telling is a factor of.

So, this one I just did, they say (x+3) is a factor of... would c automatically be +3?

The answer turned out to be +3.

Can someone give me another similar example to try?

Work some examples out for yourself.

What is (x-3)(x+4) ?

The one you were solving in this thread has a factor of (x-3).

But, suppose the question is:

If (x+3) is a factor of: x² - 4x + c, what is c?

If f(x) = x² - 4x + c, what is f(-3) ?​

 

[nukeman]

Hi sammy.

Ok, so for the question you gave me: If (x+3) is a factor of: x2 - 4x + c, what is c?

c would = -21 ?

 

[SammyS]

Hi sammy.

Ok, so for the question you gave me: If (x+3) is a factor of: x² - 4x + c, what is c?

c would = -21 ?

Yes.

 

[LCKurtz]

Hi sammy.

Ok, so for the question you gave me: If (x+3) is a factor of: x2 - 4x + c, what is c?

c would = -21 ?

Nukeman, I will suggest again, when you have a problem like that and you think c = -21 so your function is $x^2-4x-21$, why don't you just try factoring it yourself and see if x+3 is a factor instead of asking us if -21 is correct?