Question

It is given that x-2 is a factor of P(x)=2x^(3)+px^(2)+qx+8. When P(x) is divided by x+1, the remainder is 27. Find
(a) the values of p and q .
(b) the remaining factors of P(x).

Answer 1

p(1) =0
p(-1)=27

does that help ?

Answer 2

I know this

Answer 3

p-q=21 ---(1)

and the next step....

Answer 4

also make use of p(1) = 0

Answer 5

ohhh....i type the question wrongly, it should be x-2 is a factor...

Answer 6

nevermind, then it'll be p(2) =0

Answer 7

wait, let me calculate it..

Answer 8

2p+q=12---(2)

Answer 9

12 or -12 ?

Answer 10

-12

Answer 11

so you have 2 eqns, 2 variables, solve for p and q

Answer 12

p=3, q=-18

Answer 13

yep

Answer 14

(Y)

Answer 15

thanks

Answer 16

glad to help.

Answer 17

and part b ... ??

Answer 18

oh I forgot! :P

So, since you know p and q, you know P(x) right?

Answer 19

yup.

Answer 20

long division?

Answer 21

One root of this you already know is 2

Answer 22

Well yes, long division would do the job

Answer 23

There is an alternative also though, you must be knowing sum of roots = -b/a, sum in pairs = c/a , product = -d/a
??

Answer 24

ohh...after the long division, do i need to factorize it?

Answer 25

ohhh, i hate sum and product of root /.\

Answer 26

Its up to you which method you want to follow
and yes, after long division, you'll have to factorize

Answer 27

thanks

Answer 28

WADECUM !

Answer 29

(x-2)(2x-1)(x+4) ?

Answer 30

yep..seems right!