Question

on dividing 4 x^3 - 8 x^2 + 8 x + 1 by a polynomial g(x) the quotient and remainder when (2 x^2 - 3 x + 2) and X + 3 respectively find g(x)

Answer 1

Answer:So reminder is (3-x)

Step-by-step explanation:

Dividend=quotient × divisor +reminderLet g(x) is the quotient when we divide f(x) by (x-1) and h(x) is the quotient when we divide f(x) by (x-2) then we can write like f(x)=g(x)(x-1)+2Multiply both sides with (x-2).f(x)(x-2)=g(x)(x-1)(x-2)+2(x2) ……(A)f(x)=h(x)(x-2)+1Multiply both sides with (x-1).f(x)(x-1)=h(x)(x-2)(x-1)+(x-1) …..(B)Subtract A from Bf(x)(x-1-x+2)=(x-1)(x-2)(h(x)-g(x))+(x-1-2x+4)f(x)×1=(x-1)(x-2)(q(x))+(3-x)Here q(x)=(h(x)-g(x)) is the quotient when we divide it by (x-1)(x-2)