Divide Using Long Polynomial Division (2x^4+x^3-19x^2+18x+5)÷(2x-5)

$(2 x^{4} + x^{3} - 19 x^{2} + 18 x + 5) \div (2 x - 5)$

Step 1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

Step 2

Divide the highest order term in the dividend $2 x^{4}$ by the highest order term in divisor $2 x$ .

$x^{3}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

Step 3

Multiply the new quotient term by the divisor.

$x^{3}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $2 x^{4} - 5 x^{3}$

$x^{3}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

Step 5

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

Step 6

Pull the next terms from the original dividend down into the current dividend.

$x^{3}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

Step 7

Divide the highest order term in the dividend $6 x^{3}$ by the highest order term in divisor $2 x$ .

$x^{3}$

$3 x^{2}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

Step 8

Multiply the new quotient term by the divisor.

$x^{3}$

$3 x^{2}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $6 x^{3} - 15 x^{2}$

$x^{3}$

$3 x^{2}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

Step 10

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$3 x^{2}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

Step 11

Pull the next terms from the original dividend down into the current dividend.

$x^{3}$

$3 x^{2}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

$18 x$

Step 12

Divide the highest order term in the dividend $- 4 x^{2}$ by the highest order term in divisor $2 x$ .

$x^{3}$

$3 x^{2}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

$18 x$

Step 13

Multiply the new quotient term by the divisor.

$x^{3}$

$3 x^{2}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

$18 x$

$4 x^{2}$

$10 x$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 4 x^{2} + 10 x$

$x^{3}$

$3 x^{2}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

$18 x$

$4 x^{2}$

$10 x$

Step 15

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$3 x^{2}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

$18 x$

$4 x^{2}$

$10 x$

$8 x$

Step 16

Pull the next terms from the original dividend down into the current dividend.

$x^{3}$

$3 x^{2}$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

$18 x$

$4 x^{2}$

$10 x$

$8 x$

$5$

Step 17

Divide the highest order term in the dividend $8 x$ by the highest order term in divisor $2 x$ .

$x^{3}$

$3 x^{2}$

$2 x$

$4$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

$18 x$

$4 x^{2}$

$10 x$

$8 x$

$5$

Step 18

Multiply the new quotient term by the divisor.

$x^{3}$

$3 x^{2}$

$2 x$

$4$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

$18 x$

$4 x^{2}$

$10 x$

$8 x$

$5$

$8 x$

$20$

Step 19

The expression needs to be subtracted from the dividend, so change all the signs in $8 x - 20$

$x^{3}$

$3 x^{2}$

$2 x$

$4$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

$18 x$

$4 x^{2}$

$10 x$

$8 x$

$5$

$8 x$

$20$

Step 20

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$3 x^{2}$

$2 x$

$4$

$2 x$

$5$

$2 x^{4}$

$x^{3}$

$19 x^{2}$

$18 x$

$5$

$2 x^{4}$

$5 x^{3}$

$6 x^{3}$

$19 x^{2}$

$6 x^{3}$

$15 x^{2}$

$4 x^{2}$

$18 x$

$4 x^{2}$

$10 x$

$8 x$

$5$

$8 x$

$20$

$25$

Step 21

The final answer is the quotient plus the remainder over the divisor.

$x^{3} + 3 x^{2} - 2 x + 4 + \frac{25}{2 x - 5}$

Divide Using Long Polynomial Division (2x^4+x^3-19x^2+18x+5)÷(2x-5)

Related Questions

Support LCMGCF.com by disabling your adblocker.