Dividing by Monomials
Example: $\frac{24x^5}{8x^2}$
Example: $\frac{24m^4 - 18m^3 + 36m^2 - 6m}{3m}$
General Polynomial Division
- Step 1. Write the polynomials in long-division format, expressing each in standard form.
- Step 2. Divide the first term of the divisor into the first term of the dividend. The result is the first term of the quotient.
- Step 3. Multiply the first term of the quotient by every term in the divisor, and write this product under the dividend, aligning like terms.
- Step 4. Subtract this product from the dividend, and bring down the next term.
- Step 5. Use the result of step 4 as a new dividend, and repeat steps 2 through 4 until either the remainder is 0 or the degree of the remainder is less than the degree of the divisor.
Examples: perform polynomial long division to get the quotient and remainder. $$2x+7 \,\, \overline{)\,\,\,8x^3+22x^2-23x-11\,\,\,\,\,}$$ $$-8x^2+9x+4 \,\, \overline{)\,\,\,32x^3+36x^2-97x-30\,\,\,\,\,}$$ $$2x^2-x-3 \,\, \overline{)\,\,\,-8x^3+16x^2-3x-17\,\,\,\,\,}$$ $$2x-6 \,\, \overline{)\,\,\,-18x^2+66x-28\,\,\,\,\,}$$