#### Question

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg q(x) = deg r(x)

#### Solution

According to the division algorithm, if p(x) and g(x) are two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = g(x) × q(x) + r(x),

where r(x) = 0 or degree of r(x) < degree of g(x)

Degree of a polynomial is the highest power of the variable in the polynomial.

deg q(x) = deg r(x)

Let us assume the division of x^{3}+ x by x^{2}

Here, p(x) = x^{3} + x

g(x) = x^{2 }

q(x) = x and r(x) = x

Clearly, the degree of q(x) and r(x) is the same i.e., 1.

Checking for division algorithm,

p(x) = g(x) × q(x) + r(x)

x^{3} + x = (x^{2} ) × x + x

x^{3} + x = x^{3} + x

Thus, the division algorithm is satisfied.

Is there an error in this question or solution?

Solution Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm deg q(x) = deg r(x) Concept: Division Algorithm for Polynomials.