How do you divide #(6x^3-12x^2-5x+3) / (6x-9)# using long division?

Question

Isaiah Anthony · Accepted Answer

#x^2-1/2x-19/12-45/(5(6x-9))#

Start point#" "->" "6x^3-12x^2-5x+3# #color(red)(x^2)(6x-9) ->" "ul(6x^3-9x^2) larr" Subtract"# #" "0-3x^2-5x+3# #color(red)(-1/2x)(6x-9)->" " ul(-3x^2+9/2x) larr" Subtract"# #" "0 -19/2x+3# #color(red)(-19/12)(6x-9)->" "ul( -19/2x+57/4) larr" Subtract"# #" "color(red)(0 -45/5 larr" Remainder")#

In this case,

#color(blue)((6x^3-12x^2-5x+3)/(6x-9)" "=" ")color(red)(x^2-1/2x-19/12-45/(5(6x-9))#

Eva Adamson · Answer

undefined To divide (6x^3-12x^2-5x+3) by (6x-9) using long division, follow these steps:

1. Divide the first term of the dividend (6x^3) by the first term of the divisor (6x). The result is x^2.

2. Multiply the divisor (6x-9) by the quotient obtained in step 1 (x^2). The result is 6x^3-9x^2.

3. Subtract the product obtained in step 2 from the dividend (6x^3-12x^2-5x+3). This gives -3x^2-5x+3.

4. Bring down the next term from the dividend (-5x).

5. Divide the new dividend (-3x^2-5x+3) by the first term of the divisor (6x). The result is -1/2x.

6. Multiply the divisor (6x-9) by the quotient obtained in step 5 (-1/2x). The result is -3x+9/2.

7. Subtract the product obtained in step 6 from the new dividend (-3x^2-5x+3). This gives -3x^2+2x+3/2.

8. Bring down the next term from the dividend (3/2).

9. Divide the new dividend (-3x^2+2x+3/2) by the first term of the divisor (6x). The result is -1/4.

10. Multiply the divisor (6x-9) by the quotient obtained in step 9 (-1/4). The result is -3/2+9/4.

11. Subtract the product obtained in step 10 from the new dividend (-3x^2+2x+3/2). This gives 0.

The final result of the division is x^2 - 1/2x - 1/4, with no remainder.