A polynomial question...pretty challenging, please help if you can. (1 Viewer)

[js0ul]

"The polynomial P(x) is divded by (x-1)(x+2). Find the remainder, given that P(1) = 2 and P(-2)=5"

I understand that P(1) = 2 means that when the P(x) is divided by (x-1) the remainder is 2, but I do not know how to do this question. Someone please help me with this. Thankyou so much. ^^

 

[pLuvia]

The general form of a remainder is R(x)=ax+b, where a and b are constants. Use this and you should get your answer

 

[Riviet]

Note that the remainder could also be a constant, since the degree of the remainder is always less than the degree of the divisor (what you are dividing by). Since the degree of (x-1)(x+2) is a quadratic (of degree 2), the remainder could be a constant (of degree 0) OR linear (of degree 1).