use long division

Question

(2x^3+5x^2+17x+4)divided by(2x-1)

Answer 1

Set up this problem just like you would if it did not have any x's.

2x - 1 ) 2 x³ - 5 x² + 17 x + 4 Pay attention to the dividend (that's the one UNDER the bar.

Note that there are no missing exponents. 3, 2, 1, constant.

If one was missing, we would have to insert a 0 in that spot.

I am sure you will have a problem like that soon.

Now we begin the division process. Look at the 2x. Ask yourself, what must I multiply it by to get 2x³

Put that answer above the 2x³.

x²

2x - 1 ) 2 x³ - 5 x² + 17 x + 4 Multiply the x² by the divisor (2x - 1).

Line the answer up with each of the like terms in the dividend.

x²

2x - 1 ) 2 x³ - 5 x² + 17 x + 4

2 x³ - 1 x² Now subtract. Remember that subtraction means add the opposite.

-4 x² + 17x 2 x³ - 2 x³ = 0. and -5 x² - (-1 x²) = -4 x². Bring down the 17x.

Take a breath and start again. What is 2x multiplied by to give - 4 x²?

Answer is - 2 x. Put that on top.

x² - 2 x

2x - 1 ) 2 x³ - 5 x² + 17 x + 4

2 x³ - 1 x²

-4 x² + 17x Multiply -2x by the divisor. Put the answer at bottom.

-4 x² + 2x -2x ( 2x ) = -4x ² and -2x ( -1) = + 2x.

Now subtract. - 4 x² - (-4 x²) = 0 and 17x - (2x) = 15x

Bring down the 4.

x² - 2 x

2x - 1 ) 2 x³ - 5 x² + 17 x + 4

2 x³ - 1 x²

-4 x² + 17x

-4 x² + 2x

15x + 4 Take a breath and start again. Ask what is 2x multiplied by to give

15x ? Answer is 7.5. Put that on top.

x² - 2 x + 7.5

2x - 1 ) 2 x³ - 5 x² + 17 x + 4

2 x³ - 1 x²

-4 x² + 17x

-4 x² + 2x

15x + 4 Multiply 7.5 by the divisor. Put the answer at bottom.

15 x - 7.5 7.5 ( 2x ) = 15x. and 7.5 ( -1) = -7.5

11.5 Now subtract. 15x - (15 x) = 0 and 4 - (-7.5) = 11.5

You are done. Your answer is x² - 2 x + 7.5 with remainder 11.5.

You may check it by multiplying the quotient and divisor, then adding the remainder. If you get the dividend, you know your answer is correct. Does (2x - 1 ) (x² - 2 x + 7.5) + 11.5 = 2 x³ - 5 x² + 17 x + 4? Yes.

Whew!!