Question

when p(x)=x^2 + ax -b is divided by x-1, the remainder is -6. when p(x) is divided by x+2. the remainder is 3. find the values of a and b.

Answer 1

@phi pls help

Answer 2

Simple... if f(x) is any polynomial, the remainder when f(x) is divided by x-c
is equal to f(c)

Answer 3

how?

Answer 4

Let me do the first bit for you...
In the case of x - 1, c = 1, right?

Answer 5

yup

Answer 6

Right... Now, to get the remainder when p(x) is divided by x-1
it is simply p(1)

Now what is p(1) equal to?

Answer 7

x=1

Answer 8

I mean, plug in x = 1
in p(x)

Replace all the x's with 1.

Answer 9

I don't get it, sorry

Answer 10

@derek11111
I'm going out on a limb here and assuming that you're given the same question....

Get over here :P

Answer 11

http://www.purplemath.com/modules/remaindr.htm

Answer 12

xd, ahahah

Answer 13

HAHAHHAA

Answer 14

\[p(x) / (x-a) = q(x) + r(x) \]
where r(x) is the remainder

Answer 15

so
\[p(x) = q(x)(x-a) + r(x)\]

Answer 16

now if you plug in p(x) x=a you get the remainder.

Answer 17

Now listen up, the two of you -.-
To get the remainder of a polynomial p(x) when it's divided by x - c
You simply evaluate that polynomial at x = c
p(c)

In this case, we are dividing by x - 1
So c = 1

Now...
\[\Large p(\color{red}x)=\color{red}x^2 + a\color{red}x - b\]

Answer 18

So...
\[\Large p(\color{red}1) = \color{red}1^2 + a(\color{red}1) -b\]

Answer 19

so for your case,
p(x)=x^2 + ax -b divided by x-1 gives remainder of -6

so
p(1) = -6

Answer 20

but look at the website or my first responses
so youll understand why this is true.

Answer 21

what is the value of a and b? o.O?

Answer 22

you will get two equations :
p(1) = -6
and
p(-2) = 3

Answer 23

using them youll find a and b.

Answer 24

more important is to understand why it is working though.

Answer 25

can you please tell me how to find a and b using those 2

Answer 26

p(1) = 1+a-b
so since p(1) = -6
1+a-b=-6
a-b=-7
p(-2) = 4-2a-b
so since p(-2) = 3
4-2a-b=3
-2a-b=-1

you have two equations :
a-b=-7
-2a-b=-1

you can subtract one from the other and find b.
then plug b into one of them and find a.

Answer 27

how to subtract a-b= -7 from -2a-b= -1?

Answer 28

subtract each side :
-2a - b -(a-b) = -1 - (-7)
-2a - a = 6
-3a = 6
a = -2

Answer 29

thank you :)

Answer 30

when you find b, verify your answer

Answer 31

i might done some calculation mistake

Answer 32

where?

Answer 33

i dont say i did..
i might.. that is why you better verify your answer
(check that p(1) really comes out as -6 )

Answer 34

b= -3 am I right?

Answer 35

no, if a =-2
then b = 5

Answer 36

now I know how to do it thanks :)