anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@phi pls help
terenzreignz
  • terenzreignz
Simple... if f(x) is any polynomial, the remainder when f(x) is divided by x-c is equal to f(c)
anonymous
  • anonymous
how?

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terenzreignz
  • terenzreignz
Let me do the first bit for you... In the case of x - 1, c = 1, right?
anonymous
  • anonymous
yup
terenzreignz
  • terenzreignz
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?
anonymous
  • anonymous
x=1
terenzreignz
  • terenzreignz
I mean, plug in x = 1 in p(x) Replace all the x's with 1.
anonymous
  • anonymous
I don't get it, sorry
terenzreignz
  • terenzreignz
@derek11111 I'm going out on a limb here and assuming that you're given the same question.... Get over here :P
anonymous
  • anonymous
http://www.purplemath.com/modules/remaindr.htm
anonymous
  • anonymous
xd, ahahah
anonymous
  • anonymous
HAHAHHAA
anonymous
  • anonymous
\[p(x) / (x-a) = q(x) + r(x) \] where r(x) is the remainder
anonymous
  • anonymous
so \[p(x) = q(x)(x-a) + r(x)\]
anonymous
  • anonymous
now if you plug in p(x) x=a you get the remainder.
terenzreignz
  • terenzreignz
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... \[\Large p(\color{red}x)=\color{red}x^2 + a\color{red}x - b\]
terenzreignz
  • terenzreignz
So... \[\Large p(\color{red}1) = \color{red}1^2 + a(\color{red}1) -b\]
anonymous
  • anonymous
so for your case, p(x)=x^2 + ax -b divided by x-1 gives remainder of -6 so p(1) = -6
anonymous
  • anonymous
but look at the website or my first responses so youll understand why this is true.
anonymous
  • anonymous
what is the value of a and b? o.O?
anonymous
  • anonymous
you will get two equations : p(1) = -6 and p(-2) = 3
anonymous
  • anonymous
using them youll find a and b.
anonymous
  • anonymous
more important is to understand why it is working though.
anonymous
  • anonymous
can you please tell me how to find a and b using those 2
anonymous
  • anonymous
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.
anonymous
  • anonymous
how to subtract a-b= -7 from -2a-b= -1?
anonymous
  • anonymous
subtract each side : -2a - b -(a-b) = -1 - (-7) -2a - a = 6 -3a = 6 a = -2
anonymous
  • anonymous
thank you :)
anonymous
  • anonymous
when you find b, verify your answer
anonymous
  • anonymous
i might done some calculation mistake
anonymous
  • anonymous
where?
anonymous
  • anonymous
i dont say i did.. i might.. that is why you better verify your answer (check that p(1) really comes out as -6 )
anonymous
  • anonymous
b= -3 am I right?
anonymous
  • anonymous
no, if a =-2 then b = 5
anonymous
  • anonymous
now I know how to do it thanks :)

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