Question

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in each of the following:

(i) f(x) = 4x³ + 8x + 8x² + 7, g(x) = 2x² - x + 1

(ii) f(x) = 15x³ - 20x² + 13x - 12, g(x) = 2 - 2x + x²

Answer 1

(i) f(x) = 4x³ + 8x + 8x² + 7 and g(x) = 2x² - x + 1

Degree of f(x) = is 3 and degree of g(x) is 2; therefore degree of and degree of q(x) is 3 - 2 = 1 remainder is less than 2,

Let q(x) = ax + b and r(x) = cx + d

By applying division algorithm:

Dividend = Quotient× Divisor + Remainder

f(x) = q(x) x g(x) + r(x)

On substituting values in the above relation we get,

On comparing coefficients we get,

On solving above equations we get,

a = 2, b = 5, c = 11, d = 2

On substituting these values for q(x) and r(x)

(ii) f(x) = 15x³ - 20x² + 13x - 12 and g(x) = 2 - 2x + x²

Degree of f(x) = is 3 and degree of g(x) is 2; therefore degree of and degree of q(x) = is 3 - 2 = 1 remainder is less than 2,

Let q(x) = ax + b and r(x) = cx + d

By applying division algorithm:

Dividend = Quotient× Divisor + Remainder

f(x) = q(x) x g(x) + r(x)

On substituting values in the above relation we get,

On comparing coefficients we get,

On solving above equations we get,

a = 2, b = 10, c = 3,d = - 32

On substituting these values for