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

## Homework Statement

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

## 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.

Related Precalculus Mathematics Homework Help News on Phys.org
Mark44
Mentor

## Homework Statement

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

## 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
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

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

## 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 ?"

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
Homework Helper
Gold Member
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
Staff Emeritus
Homework Helper
Gold Member
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.)

Oh, I wrote on my paper 4(4)

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
Staff Emeritus
Homework Helper
Gold Member

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) ?​

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
Staff Emeritus
Homework Helper
Gold Member
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