If xcube + x square -2x-3=(x-2)(x square +ax+b) +5 then find the value

1.	If xcube + x square -2x-3=(x-2)(x square +ax+b) +5 then find the values of a and b.
Answer» => x^3 + x^2 - 2x -3 - 5 = (x-2)(x^2+ax+b)=> x^3 + x^2 - 2x - 8 = (x-2)(x^2+ax+b) At x = 2, x^3 + x^2 - 2x - 8 = 0=> (x - 2) is a factor of x^3 + x^2 - 2x - 8; Dividing x^3 + x^2 - 2x - 8 by (x-2), we get ---(x-2)(x^2+3x+4) = (x-2)(x^2+ax+b) => x^2+3x+4 = x^2+ax+b Comparing the co-efficients, we get a = 3 , b = 4 -------------- Ans x^3 + x^2 - 2x - 3 -------- where ^ represents raise to the power. => x^3 + x^2 - 2x -3 - 5 = (x-2)(x^2+ax+b)=> x^3 + x^2 - 2x - 8 = (x-2)(x^2+ax+b) At x = 2, x^3 + x^2 - 2x - 8 = 0=> (x - 2) is a factor of x^3 + x^2 - 2x - 8; Dividing x^3 + x^2 - 2x - 8 by (x-2), we get ---(x-2)(x^2+3x+4) = (x-2)(x^2+ax+b) => x^2+3x+4 = x^2+ax+b Comparing the co-efficients, we get a = 3 , b = 4

If xcube + x square -2x-3=(x-2)(x square +ax+b) +5 then find the values of a and b.

Answer»

=> x^3 + x^2 - 2x -3 - 5 = (x-2)(x^2+ax+b)=> x^3 + x^2 - 2x - 8 = (x-2)(x^2+ax+b)

At x = 2, x^3 + x^2 - 2x - 8 = 0=> (x - 2) is a factor of x^3 + x^2 - 2x - 8;

Dividing x^3 + x^2 - 2x - 8 by (x-2), we get ---(x-2)(x^2+3x+4) = (x-2)(x^2+ax+b)

=> x^2+3x+4 = x^2+ax+b

Comparing the co-efficients, we get

a = 3 , b = 4 -------------- Ans

x^3 + x^2 - 2x - 3 -------- where ^ represents raise to the power.

=> x^3 + x^2 - 2x -3 - 5 = (x-2)(x^2+ax+b)=> x^3 + x^2 - 2x - 8 = (x-2)(x^2+ax+b)

At x = 2, x^3 + x^2 - 2x - 8 = 0=> (x - 2) is a factor of x^3 + x^2 - 2x - 8;

Dividing x^3 + x^2 - 2x - 8 by (x-2), we get ---(x-2)(x^2+3x+4) = (x-2)(x^2+ax+b)

=> x^2+3x+4 = x^2+ax+b

Comparing the co-efficients, we get

a = 3 , b = 4