Question

the polynomial P(x)=x^3+ax^2+3x+b has a reminder of -8 when divided by
x-3. One of the factors of p(x) is x+1. Find a and b.

Answer 1

Do you think for this question need to do system of equation?

Answer 2

i'm not sure if this is right: a=146/8 and b=98/8

Answer 3

So this is basically long division twice, which results in some algebraic equations:

Answer 4

x+1 is one factor mean x=-1 is root os equation

Answer 5

I used substitution since i found that easiest
Check my messy work here : http://www.twiddla.com/Redirector.aspx?404;http://www.twiddla.com:80/1581717

Answer 6

root will satisfy the equation and p(-1)=0
p(-1)=0=(-1)^3+a*(-1)^2+3*(-1)+b

Answer 7

----> http://prntscr.com/4rzzvr

Answer 8

You can probably use synthetic division which is neater

Answer 9

0=-1+a-3+b
0=-4+a+b
a+b=4

Answer 10

So that gives us one equation for a, b... then the next one is similar
we divide x+1 into P(x) get an expression for the remainder and set it equal to 0 in this case

Answer 11

now on dividing with x-3 it gives remainder =-8

Answer 12

----> http://prntscr.com/4s00ib

Answer 13

now if we add 8 in the equation than it will give remainder =0

Answer 14

if remainder is aero than x-3 will be its factor

Answer 15

that means x=3 is a factor of the equation

Answer 16

x^3+ax^2+3x+b +8 x=3 is a factor of this equation

Answer 17

put x=3 which should give result =0

Answer 18

3^3+a3^2+3*3+b+8=0

Answer 19

27+9a+9+b+8=0
9a+b=-44

Answer 20

http://prntscr.com/4s01em

Answer 21

9a+b=-44
a+b=4 means b=4-a putting it in above equation
9a+4-a=-44
8a+4=-44
8a=-44+4=-40
a=-40/8=-5
and b=9

Answer 22

so a=-5 and b=9

Answer 23

a = -6 @gorv

Answer 24

and b = 10

Answer 25

mine is comming -5

Answer 26

and 9

Answer 27

Well, mine came out as a= -6 and b= 10... Unless I have the wrong P(x) or factors
But given the problem statement, I'm confident in this answer now

Answer 28

I really doubt it unless I don't have the right P(x) or factors
or maybe the wrong remainder