What is the quotient when 6x3 plus 29x2 -40x -42 is divided by 6x plus 5?

Answer 1

Use long division; at each stage:

1. work out the multiplier of the divisor required to remove the highest power of x remaining in the dividend;
2. put the multiplier found in step 1 as the next term in the quotient;
3. multiply the divisor by this multiplier;
4. subtract like normal;
5. bring down the next term;
6. repeat from step 1 until there are no more terms to bring down;
7. If the result after the final subtraction and bringing down of terms is non-zero this is a remainder after the division by the divisor.

(6x³ + 29x² - 40x - 42) ÷ (6x + 5) =

__________________x² + 4x - 10

________-------------------------

6x + 5 |6x³ + 29x² - 40x - 42

_________6x³ + 5x²_______________________← x²(6x + 5)

_________------------

_______________24x² - 40x

_______________24x² +20x________________← 4x(6x + 5)

_______________--------------

____________________- 60x - 42

____________________- 60x - 50___________← -10(6x + 5)

____________________------------

_____________________________8

→ (6x³ + 29x² - 40x - 42) ÷ (6x + 5) = x² + 4x - 10 remainder 8

= (x² + 4x - 10) + 8/(6x + 5)

Answer 2

The quotient is x^2 + 4x - 10, and there is a remainder.