- #1

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## 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.

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- Thread starter nukeman
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- #1

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

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

Thanks so much.

- #2

Mark44

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## 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) = x

As it happens, f(x) can be factored into (x - 3)(x

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) = 3

- #3

SammyS

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The first thing## 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.

For this problem, "What is the remainder of (x

- #4

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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????

- #5

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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.

- #6

SammyS

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What is 4(3) ?

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????

(It's not 16.)

- #7

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Oh, I wrote on my paper 4(4)

- #8

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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???

- #9

SammyS

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Work some examples out for yourself.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???

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: x^{2} - 4x + c, what is c?

If f(x) = x^{2} - 4x + c, what is f(-3) ?

If f(x) = x

- #10

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

c would = -21 ?

- #11

SammyS

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Yes.Hi sammy.

Ok, so for the question you gave me: If (x+3) is a factor of: x^{2}- 4x + c, what is c?

c would = -21 ?

- #12

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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?

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