Question

If the polynomial `(x^(4)+2x^(3)+8x^(2)+12x+18)` is divided by another polynomial `(x^(2)+5)`, the remainder comes out to be `(px+q)`. Find the values of `p` and `q`.

Answer 1

Let `f(x) = (x^(4)+2x^(3)+8x^(2)+12x+18) and g(x) = (x^(2)+5).`
On dividing ` f(x) " by " g(x),` we get

Now, `px+q=2x+3 rArr p=2 and q=3.`