Question

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 :)

Answer 1

Q(x) is an unknown polynomial?

Answer 2

yea

Answer 3

then... a = -1, b = 2?...dont think it should be this simple

Answer 4

that isnt the answer lol

Answer 5

answer is a = 20 b = 24

Answer 6

but i cant get it :(

Answer 7

if Q(x) = 5x-9 ?

Answer 8

o..o maybe you could work out the full solution and see if it matches my answer :P

Answer 9

Thank you.

Answer 10

\[ (x+​1)*​(x+​2)*​(5*​x-​9) = 5x^3 + 6x^2 -17x - 18 + 16x +20=5x^3 + 6x^2 -x + 2\]

Answer 11

@Sgstudent

Answer 12

oo then how should i carry on

Answer 13

hmm a is 16 and b is 20 for me

Answer 14

check for any careless mistake? :O

Answer 15

no i don't think so

Answer 16

can you upload the picture of your working?

Answer 17

i didn't do it on my notebook, in head.

Answer 18

\[(x+​1)(x+​2)(5x−​9) +ax + b = 5x^3+6x^2−17x−18+ ax+b\]

Answer 19

i did it also and got same result as ishaan

Answer 20

i need the working :(

Answer 21

or rather simple explanation towards the steps

Answer 22

equating coefficients of x gives
-1 = 10 - 27 + a
a = 27-11 = 16

Answer 23

use q(x) as px +q, suggested by you earlier if you really need to show working

Answer 24

can i let Q(x) = px + q will i be able to get the answer?

Answer 25

oh but i cant seem to get the answer somehow :(

Answer 26

i get decimal numbers :(

Answer 27

show me your working i will try to guide you

Answer 28

kk i try again

Answer 29

well you can get multiple answers, maybe.

Answer 30

only a and b

Answer 31

(x+1) (x-2) *********

Answer 32

Ishaan i edited the question

Answer 33

sry about it

Answer 34

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

Answer 35

Thanks :)

Answer 36

yw