Divide: (6x^3 - x^2 -10) / (3x + 4)?

Question

Write answers this way:
Quotient: (polynomial expression)
Remainder: (number)

Answer 1

Rewrite the expression in long division form (6x³ - x² - 10)/(3x + 4).

Because  there  is  no x - 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 6x³/3x = 2x².

So,the first term of the quotient is  2x². Multiply (3x + 4) by  2x² and subtract.

Divide the first term of the last row by first term of the divisor -9x²/3x = -3x.

So,the second term of the quotient is (-3x). Multiply (3x + 4) by (-3x) and subtract.

Divide the first term of the last row by first term of the divisor  12x/3x = 4.

So,the third term of the quotient is 4. Multiply (3x + 4) by 4 and subtract.

Quotient Q(x) = 2x² - 3x + 4.

Remainder R(x) = - 26.