Q. 21

# Give an example of polynomials f(x), g(x), q(x) and r(x) satisfying f(x) = g(x) .q(x)+ r(x), where degree r (x) = 0.

Let

f(x) = x3 + x2 + x + 1

g(x) = x + 2

q(x) = x2 - x + 3

r (x) = -5

Now, f(x) = g(x) .q(x)+ r(x)

Here,

L.H.S = x3 + x2 + x + 1

And, R.H.S = [(x + 2) × (x2 - x + 3)] + (-5)

= x3 + 2x2 – x2 – 2x + 3x + 6 – 5

= x3 + x2 – 2x + 3x + 6 – 5

= x3 + x2 + x + 1

= R.H.S

the given set of polynomials satisfies the equation: f(x) = g(x) .q(x)+ r(x)

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