Bionomial theorem/ question (wp)

[Nelo]

Homework Statement

For what values of k does the function f(x)= x^3 + 6x^2 +kx -4 give the same remainder when divided by x-1 and x+2?

answer, however in the booklet it says the answer is 3, why is this? what did i do wrong?

Homework Equations

The Attempt at a Solution

So.. i set up two equations one using f(1) and one using f(-2)

f(1)= 1 + 6 + 1k -4
f(1) = -2 +k
2 = k

f(-2) = 12 -2k
2k = 12
k= 6,

I plugged 6 and 2 into the equation of f(1) and got the same (remainder of 9)

wat am i doing wrong?

 

[Nelo]

anyone??

 

[SammyS]

anyone??

Patience !

Please, wait at least 24 hours before bumping your thread.

 

[SammyS]

Homework Statement

For what values of k does the function f(x)= x^3 + 6x^2 +kx -4 give the same remainder when divided by x-1 and x+2?

answer, however in the booklet it says the answer is 3, why is this? what did i do wrong?

Homework Equations

The Attempt at a Solution

So.. i set up two equations one using f(1) and one using f(-2)

f(1)= 1 + 6 + 1k -4
f(1) = -2 +k This says that the remainder for f(x)/(x-1) is k - 2 .
2 = k Why do this step?

f(-2) = 12 -2k This says that the remainder for f(x)/(x+2) is 12 -2k .
2k = 12
k= 6,

I plugged 6 and 2 into the equation of f(1) and got the same (remainder of 9)

what am i doing wrong?

What does the remainder theorem say?

Set the two remainders equal to each other. Solve for k.

 

[Nelo]

wat? like.. 6k = 2?

6/2 = 3
k=3?

 

[eumyang]

So.. i set up two equations one using f(1) and one using f(-2)

f(1)= 1 + 6 + 1k -4
f(1) = -2 +k

1 + 6 - 4 = -2?

2 = k

f(-2) = 12 -2k
2k = 12
k= 6,

Where did the f(1) and f(-2) go? This makes no sense. If you're supposed to get the same remainder when dividing by x - 1 and x + 2, then that means that
f(1) = f(-2).

And can you also please double check your work before submitting your post?

 

[Nelo]

f(1)= 1 + 6 + 1k -4
f(1) = 7-4+1k
f(1) = 3+k
-3=k

f(-2) = (-2)^3 + 6(-2)^2 + k(-2) -4
f(-2) = 12 -2k
2k = 12
k= 6

?? what do i do now

 

[eumyang]

f(1)= 1 + 6 + 1k -4
f(1) = 7-4+1k
f(1) = 3+k
-3=k

Again, why are you making the f(1) disappear? DON'T DO THAT!

You say
f(1) = 3 + k
and
f(-2) = 12 - 2k.

Since the remainders are supposed to be equal,
f(1) = f(-2)
so substitute with the right-hand-side of the two previous equations.

 

[Nelo]

I don't get it... substitute something that's not a full equation into the right hand side of the prev 2 eq? doesn't something have to = k inorder for me to sub it into another equation..?

How do i substitute dat

 

[eumyang]

I don't get it... substitute something that's not a full equation into the right hand side of the prev 2 eq? doesn't something have to = k inorder for me to sub it into another equation..?

How do i substitute dat

f(1) = f(-2)
Instead of f(1), write what it equaled to.
Instead of f(-2), write what it equaled to.
That's what I meant by substituting.

 

[Nelo]

f(1) = 3 + k
and
f(-2) = 12 - 2k.


3+k = 12-2k
-9 = -3k
k= 3 ...

I see, thanks :P

 

[SammyS]

That's exactly what I suggested you do back in post #4 .

 

[Nelo]

gl bk