Question

divide the polynomial x⁴+px²+qx+5. by x²+2x+3​ by division algorithm please answer guy's​

Answer 1

Your answer is given below -:::

polynomial f(x) = x4 + 2x3 − 2x2 + x − 1 so that the resulting polynomial is exactly divisible by x2 + 2x − 3 ?

SOLUTION

We know that,

f(x) = g(x) x q(x) + r(x)

f(x) - r(x) = g(x) x q(x)

f(x) + {- r(x)} = g(x) x q(x)

Clearly , Right hand side is divisible by g(x).

Therefore, Left hand side is also divisible by g(x).Thus, if we add - r(x) to f(x), then the resulting polynomial is divisible by g(x).

Let us now find the remainder when f(x) is divided by g(x).

Hence, we should add - r(x) = x - 2 to f(x) so that the resulting polynomial is divisible by g(x).