Question

Divide the polynomial x4-9x2+9 by the polynomial x2-3x and verify the division algorithm

Answer 1

On, Dividing p(x) = x⁴ - 9x² + 9  by g(x) = x² - 3x

We get q(x) = x² + 3x  and r(x) = 9

Then Division algorithm,

p(x) = q(x) × g(x) + r(x) 

x⁴ - 9x² + 9 = (x² + 3x)(x² - 3x) + 9

x⁴ - 9x² + 9 = x⁴ - 3x³ + 3x³ - 9x² + 9

x⁴ - 9x² + 9 = x⁴ - 9x² + 9

LHS = RHS

Hence Verified //
_________________________________________________________

☺ ☺ ☺ Hope this Helps ☺ ☺ ☺

Answer 2

Answer:

On, Dividing p(x) = x⁴ - 9x² + 9  by g(x) = x² - 3x

We get q(x) = x² + 3x  and r(x) = 9

Then Division algorithm,

p(x) = q(x) × g(x) + r(x) 

x⁴ - 9x² + 9 = (x² + 3x)(x² - 3x) + 9

x⁴ - 9x² + 9 = x⁴ - 3x³ + 3x³ - 9x² + 9

x⁴ - 9x² + 9 = x⁴ - 9x² + 9

LHS = RHS

Hence Verified