Polynomials help (1 Viewer)

[cutemouse]

Hi, could someone please help me with the following question? Thanks

When the polynomial P(x) is divided by (x+1)(x-2), the result can be written as P(x)=(x+1)(x-2)Q(x) + R(x), where R(x)=ax+b

(i) Given that P(-1)=3, find the value of R(-1)

(ii) Given also that the remainder is -2 when P(x) is divided by x-2, find the values of a and b.

 

[shaon0]

i) If R(x)=ax+b when x=-1.
R(-1)=-a+b.
3=-a+b
b=3+a

ii) P(2)=R(2)
R(2)=-2
=> -2=2a+b
=> -2=2a+(3+a)
3a=-5
a=(-5/3)
b=(4/3)

 

[cutemouse]

ii) P(-2)=R(-2)

Hey, dont you mean P(2)?

Thanks

 

[shaon0]

Hey, dont you mean P(2)?

Thanks

Sorry about that.