Question

Help with polynomials 4x^3-7x-12/x-4?

Answer 1

Rewrite the expression in long division form (4x³ - 7x - 12)/(x - 4).

Because there is no x² - term in the dividend, we need to line up the subtraction by using zero coefficients (or leaving spaces) for the missing terms.

Divide the first term of the dividend by the first term of the divisor 4x³/x = 4x².

The first term of the quotient is 4x². Multiply (x - 4) by 4x² and subtract.

Divide the first term of the last row by first term of the divisor 16x²/x = 16x.

The second term of the quotient is 16x. Multiply (x - 4) by 16x and subtract.

Divide the first term of the last row by first term of the divisor  57x/x = 57.

The third term of the quotient is 57. Multiply (x - 4) by 57 and subtract.

There fore, the remainder is R = 216 and quotient is 4x² +16 x +57.

The result is (4x³ - 7x - 12)/(x - 4) = (4x² + 16x + 57) + (216/(x - 4)).