Question

When a polynomial P(x) is divided by (x − 1) and (x − 2), the remainder are 5 and 7 respectively. What is the remainder when P(x) is divided by (x^2 − 3x + 2)?

Answer 1

According to factor theoremp(x)=xq(x)+1P(x)=(x−2)q ′ (x)+3P(x)=(x−3)q ′′ (x)+2So, At x=0,P(0)=1At x=2,P(2)=3At x=3,P(3)=2Now when the polynomial P(x) is divided by (x−2)(x−3)x the remainder must have the degree less than 3 . that is the remainder will be of the form ax 2 +bx+c⟹P(x)=x(x−2)(x−3)q ′′′′ (x)+ax 2 +bx+cSo, P(0)=1=a(0) 2 +b(0)+c⟹c=1 PLZ MARK ME AS BRAINLIEST ANSWER