Question

Verify division algorithm for the polynomial `f(x)= (8 + 20x + x^2 – 6x^3) by g(x) =( 2 + 5x –3x^2).`  

Answer 1

We can write f(x) as –`6x^3 + x^2 + 20x + 8 and g(x)` as `–3x^2 + 5x + 2` 

 

Quotient = 2x + 3
Remainder = x + 2
By using division rule, we have
Dividend = Quotient × Divisor + Remainder 

∴` –6x^3 + x^2 + 20x + 8 = (–3x^2 + 5x + 2) (2x + 3) + x + 2`
⇒` –6x^3 + x^2 + 20x + 8 = –6x^3 + 10x^2 + 4x –9x^2 + 15x + 6 + x + 2`
⇒` –6x^3 + x^2 + 20x + 8 = –6x^3 + x^2 + 20x + 8 `