Question

The polynomial a(x)=x^3+5x^2+2x+3 is divided by b(x)=x^2+mx+1

Answer 1

Given :- The polynomial a(x)=x^3+5x^2+2x+3 is divided by b(x)=x^2+mx+1 .

Solution :-

I think we need to find quotient and remainder here .

dividing a(x) by b(x) by long division method we get,

x² + mx + 1 ) x³ + 5x² + 2x + 3 ( x + (5 - m)

x³ + mx² + x

(5-m)x² + x + 3

(5-m)x² + mx(5-m) + (5-m)

x - (5mx - m²x) -(5 - m)

→ Quotient = x + (5 - m)

→ Remainder = [x - (5mx - m²x) -(5 - m)] or, (m²x + x - 5mx + m - 5) .

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