Let us now extend this process to divide a polynomial by a quadratic polynomial.
Divide `3x^3 + x^2 + 2x + 5` by `1 + 2x + x^2`. Class 10 Chapter 2 Example 7
We first arrange the terms of the dividend and the divisor in the decreasing order
of their degrees. Recall that arranging the terms in this order is called writing the polynomials in
standard form. In this example, the dividend is already in standard form, and the divisor, in
standard form, is `x^2 + 2x + 1`.
Step 1 : To obtain the first term of the quotient, divide the highest degree term of the
dividend (i.e., `3x^3`) by the highest degree term of the divisor (i.e., `x^2`). This is `3x`. Then
carry out the division process. What remains is `– 5x^2 – x + 5`.
Step 2 : Now, to obtain the second term of the quotient, divide the highest degree term
of the new dividend (i.e., `–5x^2`) by the highest degree term of the divisor (i.e., `x^2`). This
gives –5. Again carry out the division process with `–5x^2 – x + 5`.
Step 3 : What remains is `9x + 10`. Now, the degree of `9x + 10` is less than the degree
of the divisor `x^2 + 2x + 1`. So, we cannot continue the division any further.
So, the quotient is` 3x – 5 `and the remainder is `9x + 10`. Also,