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Given that 5x^3 + 6x^2 -x + 2 = (x+1) (x-2) Q(x) + ax + b find the value of a and b. Question on Identities :)

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Q(x) is an unknown polynomial?
then... a = -1, b = 2?...dont think it should be this simple

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Other answers:

that isnt the answer lol
answer is a = 20 b = 24
but i cant get it :(
if Q(x) = 5x-9 ?
o..o maybe you could work out the full solution and see if it matches my answer :P
Thank you.
\[ (x+​1)*​(x+​2)*​(5*​x-​9) = 5x^3 + 6x^2 -17x - 18 + 16x +20=5x^3 + 6x^2 -x + 2\]
oo then how should i carry on
hmm a is 16 and b is 20 for me
check for any careless mistake? :O
no i don't think so
can you upload the picture of your working?
i didn't do it on my notebook, in head.
\[(x+​1)(x+​2)(5x−​9) +ax + b = 5x^3+6x^2−17x−18+ ax+b\]
i did it also and got same result as ishaan
i need the working :(
or rather simple explanation towards the steps
equating coefficients of x gives -1 = 10 - 27 + a a = 27-11 = 16
use q(x) as px +q, suggested by you earlier if you really need to show working
can i let Q(x) = px + q will i be able to get the answer?
oh but i cant seem to get the answer somehow :(
i get decimal numbers :(
show me your working i will try to guide you
kk i try again
well you can get multiple answers, maybe.
only a and b
(x+1) (x-2) *********
Ishaan i edited the question
sry about it
i can see how ishaan got p = 5 because of the 5x^3 but the q = -9 is not obvious = 5x^3 + 15x^2 + 10x + qx^2 + 3qx + 2q + ax + b = 5x^3 + (15 + q)x^2 + (10 + 3q + a)x + 2q + b compare coefficients with 5x^3 + 6x^2 - x + 2 of x^2: q + 15 = 6 so q = -9 of x: 10 + a + 3q = 10 + a - 27 = a - 17 and a -17 = -1 so a = 16 of x^0 : 2q + b = 2 so -18 + b = 2 so b = 20 a=16, b = 20
Thanks :)

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