Final answer:
Polynomial long division is a method to divide polynomials, similar to long division with numbers, by dividing the coefficients and subtracting the exponents of like terms.
Step-by-step explanation:
The process of polynomial long division involves dividing the terms of the dividend by the divisor while subtracting the exponents. To perform polynomial long division, you align the terms of the polynomial in descending order of degree, divide the first term of the dividend by the first term of the divisor, and then subtract this result multiplied by the divisor from the dividend. This process continues until all the terms have been divided.
For example, when dividing 10x⁴ by -5x², you would divide the coefficients (10/(-5) = -2) and subtract the exponents (4 - 2 = 2), resulting in -2x² as the first term of the quotient. Repeat this process with the new polynomial that results from the subtraction step until you've worked through all the terms of the original dividend.