Factor and Remainder Theorem

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This is the project we made in our mathematics subject. It took us one day to do this.

Transcript of Factor and Remainder Theorem

Page 1: Factor and Remainder Theorem

Remainder and Factor Theorem

Page 2: Factor and Remainder Theorem

One Day....

Page 3: Factor and Remainder Theorem

Jake! What’s for breakfast?

Page 4: Factor and Remainder Theorem

Anything that has anything, Finn.

Page 5: Factor and Remainder Theorem

What are you doing now, man?

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Putting anything to this thing.

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VOILA!!!

Page 8: Factor and Remainder Theorem

I hope it tastes great, you know I love food more

than I love people.

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Gimme some, man.

Page 10: Factor and Remainder Theorem

THERE’S SOMETHING

BEHIND YOU, MAN!

Page 11: Factor and Remainder Theorem

Should… I… move?!?!

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Page 13: Factor and Remainder Theorem

VENGEANCE I THIRST FOR, VENGEANCE I MUST GET!!!

Finn the human, Jake the Dog, you will be my

Prisoners Forever!

Page 14: Factor and Remainder Theorem

WOOOS

H!!

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AAAAAHHHHHHHHHH!!!

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Plop!

OUCH! That hurts!!TSK.

CRASH!

Page 17: Factor and Remainder Theorem

Hey, Jake! Where are we?!

I don’t know bud.But I remember

the Lich King

Page 18: Factor and Remainder Theorem

YES! THAT LICH KING! And I remember him

saying about Prisoners…

And…something about, *GASP!*

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FOREVER!FOREVER!

Page 20: Factor and Remainder Theorem

Are you thinking what I’m thinking

Jake? Yes Finn, I know what

you’re thinking.

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ITS…

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Page 23: Factor and Remainder Theorem

Hey Jake! There’s something different

on that wall!Oh yeah pal! I can see that!

Page 24: Factor and Remainder Theorem

Hey Jake! There’s something different

on that wall!Oh yeah pal! I can see that!

Page 25: Factor and Remainder Theorem

WOOOS

H!!

Page 26: Factor and Remainder Theorem

You can never

escape from me, Finn and

Jake.

Page 27: Factor and Remainder Theorem
Page 28: Factor and Remainder Theorem

CREEPY…

Let’s take a closer look at the wall

Jake.. Ignore the Lich.

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F I n d t dhe Le Tt eR s A n s w e R t-h E N u mBe rS

Page 30: Factor and Remainder Theorem

Find the Letters! Answer the numbers!

Page 31: Factor and Remainder Theorem
Page 32: Factor and Remainder Theorem

How to find the remainder when f(x) = (x+3)(x2-5x+3) is divided by (x-3)

Page 33: Factor and Remainder Theorem

To find the remainder, we

must follow what the remainder

theorem states.

Page 34: Factor and Remainder Theorem

It states that if c is a number and the

polynomial P(x) is divided by x-c, then the

remainder is P(c) where P(c) is the value of the polynomial P(x)

when x = c.

Page 35: Factor and Remainder Theorem

So, if we follow the remainder theorem, it will

be P(3)=[(3)+3][(3)2-5(3)+3]

Page 36: Factor and Remainder Theorem

And the final answer

will be -18!!!

Page 37: Factor and Remainder Theorem

So, we will take 18 steps

to the left because of

the negative sign.

Page 38: Factor and Remainder Theorem

WWOOOHHH!!

Next one please!

Page 39: Factor and Remainder Theorem
Page 40: Factor and Remainder Theorem

Find the remainder

when x5-4x4+5x2-3x+2 is divided by

(x-3).

Page 41: Factor and Remainder Theorem

That’s a piece of cake! Again to find the remainder, we

must follow the statement in remainder theorem.

Page 42: Factor and Remainder Theorem

It will be P(3)=[(3)5-

4(2)4+5(2)2-3(2)+2]and the answer that we can get

is -43

Page 43: Factor and Remainder Theorem

Therefore, we will take 43 steps again to the left

since our answer is negative.

Page 44: Factor and Remainder Theorem
Page 45: Factor and Remainder Theorem

What value of k will make (x-3) a factor of

f(x) = x3+2x2+kx-12

Page 46: Factor and Remainder Theorem

Hey? I think it has something to do with factor theorem which

states that a given polynomial P(x), (x-c) is

a factor of P(x) if and only if P(c) = 0.

Page 47: Factor and Remainder Theorem

Using the factor theorem the equation

will be:f(3) = x3+2x2+kx-12

Page 48: Factor and Remainder Theorem

f(3) = x3+2x2+kx-120 = (3)3+2(3)2+3k-

120 = 27 +18 + 3k –

12-3k=33

K = -11

Page 49: Factor and Remainder Theorem

So we will take 11 steps

to the left

Page 50: Factor and Remainder Theorem
Page 51: Factor and Remainder Theorem

Find the value of k so that

x3+2x2kx+3 will leave a remainder of 5 when divided

by x-2

Page 52: Factor and Remainder Theorem

G(2) = (2)3+2(2)2-2k+3

G(2) = 58 + 8 - 2k + 3 = 5

-2k= -14K = 7

Page 53: Factor and Remainder Theorem

We will take 7 steps to the right.

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Page 55: Factor and Remainder Theorem

We’re almost near pal…

there’s another letter

there dude

Yes Jake… We can do this...

Page 56: Factor and Remainder Theorem

Determine the value of K so that P(2) =

2 for P(x) = kx4+2x3-36x+10

Page 57: Factor and Remainder Theorem

Using the remainder theorem,

substitute the value of the divisor.

Page 58: Factor and Remainder Theorem

So it will be,P(2) = k(2)4+2(2)3-36(2)+10

P(2) = 22= 16k + 16 - 72 + 10

46+2 = 16k 48 = 16k

3 = k

Page 59: Factor and Remainder Theorem

The value of k is 3!So, we will take 3 steps to the right.

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OH man! I can see the light

Finn!

Another successful adventure! In your

face LICH KING!

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YEEEESSS!!!

Page 63: Factor and Remainder Theorem

AT LAST! WE GOT OUT!

Page 64: Factor and Remainder Theorem

Courtesy to Cartoon Network&

THE CREATOR OF ADVENTURE TIME!

Page 65: Factor and Remainder Theorem

SUBMITTED BY:Daizelle Ann P. AngadolJason Ryan A. RamosMerianne O. Santos

IV-Diamond

Page 66: Factor and Remainder Theorem

Find the remainder when f(x) =

(x+3)(x2-5x+3) is divided by (x-3). Negative is to left, positive

to right.

Back

Page 67: Factor and Remainder Theorem

Find the remainder

when x5-4x4+5x2-3x+2 is divided by

(x-3).

BACK

Page 68: Factor and Remainder Theorem

Find the value of k that will make (x-3) a

factor of f(x) =

x3+2x2+kx-12

Back

Page 69: Factor and Remainder Theorem

Determine the value of K so that P(2) = 2

for P(x) = kx4+2x3-36x+10

BACK


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