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Functions (As Maths)

I remember my teacher showing us two ways to do this and he specifically told to use one method for certain cases but I can't remember either and I'm stuck on this question. I'd love some help.
I'll post the question (8) below.
Reply 1
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Original post by A0W0N
...

f(2)=0f(2) = 0 means if you substitute in x=2x=2 into f(x)f(x) then equate it to zero, you end up with an equation in two variables b,cb,c.

Now, if you use similar information regarding division by (x+3)(x+3), you end up with another equation in b,cb,c.

Hence, you would end up solving a pair of simultaneous equations for b,cb,c.

So the question is this ... are you familiar with the Remainder Theorem?
Reply 3
Original post by RDKGames
f(2)=0f(2) = 0 means if you substitute in x=2x=2 into f(x)f(x) then equate it to zero, you end up with an equation in two variables b,cb,c.

Now, if you use similar information regarding division by (x+3)(x+3), you end up with another equation in b,cb,c.

Hence, you would end up solving a pair of simultaneous equations for b,cb,c.

So the question is this ... are you familiar with the Remainder Theorem?

image.jpg
is this correct so far? I think i remember the remainder theorem
Original post by A0W0N
is this correct so far? I think i remember the remainder theorem

16+2b+c=016+2b+c = 0 is correct.

I am not sure why you are trying to divide this expression by x+3 though. Just leave it alone.

Well, look through your notes or textbook. What does the remainder theorem say ?
Reply 5
Original post by RDKGames
16+2b+c=016+2b+c = 0 is correct.

I am not sure why you are trying to divide this expression by x+3 though. Just leave it alone.

Well, look through your notes or textbook. What does the remainder theorem say ?

that once it is divided it will equal the equation
Let factor = a
If f(x)/(x+3) = a and remainder 85
f(x) = a(x+3) + 85

Let x = -3...
Reply 7
Original post by RDKGames
16+2b+c=016+2b+c = 0 is correct.

I am not sure why you are trying to divide this expression by x+3 though. Just leave it alone.

Well, look through your notes or textbook. What does the remainder theorem say ?

that f(1) is equal the the remainder
Reply 8
Original post by MindMax2000
Let factor = a
If f(x)/(x+3) = a and remainder 85
f(x) = a(x+3) + 85

Let x = -3...

I'm sorry but I'm really confused
Reply 9
Original post by A0W0N
I'm sorry but I'm really confused

If f(x) divided by x+3 leaves remainder 85 then you can write

f(x) = (x+3)a(x) + 85 for some polynomial a(x).

Can you see why setting x = -3 here is a useful thing to do?
Original post by A0W0N
I'm sorry but I'm really confused

Let x =-3
f(-3) = a(-3+3) + 85
f(-3) = a(0) +85
f(-3) = 85

i.e. c = 85...

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