Question

Use the long division method to find the result when 3x4 + 2x³ - 7x² - 12x - 2is divided by x² - 2x + 1. If there is a remainder, express the result in the formq(x) +b(x)

Answer 1

The long division method for polynomials makes use of the same procedure as the regular division of numbers. We divide the first term of the dividend by the first term of the divisor, multiply the quotient and the divisor, then subtract the product from the dividend, and then repeat the process.

The answer is:

`3x^2+8x+6+(-8x-8)/(x^2-2x+1)`

which can also be written as:

`3x^2+8x+6-(8x+8)/(x^2-2x+1)`

If you subtract the remainder, then the numerator will become 8x + 8.

`-8x-8=-(8x+8)`