Divide Using Long Polynomial Division (m^5-3m^2-20)÷(m-2)

$(m^{5} - 3 m^{2} - 20) \div (m - 2)$

Step 1

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

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

Step 2

Divide the highest order term in the dividend $m^{5}$ by the highest order term in divisor $m$ .

$m^{4}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

Step 3

Multiply the new quotient term by the divisor.

$m^{4}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

Step 4

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

$m^{4}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

Step 5

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

$m^{4}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

Step 6

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

$m^{4}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

Step 7

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

$m^{4}$

$2 m^{3}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

Step 8

Multiply the new quotient term by the divisor.

$m^{4}$

$2 m^{3}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

Step 9

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

$m^{4}$

$2 m^{3}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

Step 10

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

$m^{4}$

$2 m^{3}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

Step 11

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

$m^{4}$

$2 m^{3}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

Step 12

Divide the highest order term in the dividend $4 m^{3}$ by the highest order term in divisor $m$ .

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

Step 13

Multiply the new quotient term by the divisor.

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $4 m^{3} - 8 m^{2}$

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

Step 15

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

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

Step 16

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

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

$0 m$

Step 17

Divide the highest order term in the dividend $5 m^{2}$ by the highest order term in divisor $m$ .

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$5 m$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

$0 m$

Step 18

Multiply the new quotient term by the divisor.

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$5 m$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

$0 m$

$5 m^{2}$

$10 m$

Step 19

The expression needs to be subtracted from the dividend, so change all the signs in $5 m^{2} - 10 m$

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$5 m$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

$0 m$

$5 m^{2}$

$10 m$

Step 20

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

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$5 m$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

$0 m$

$5 m^{2}$

$10 m$

Step 21

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

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$5 m$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

$0 m$

$5 m^{2}$

$10 m$

$20$

Step 22

Divide the highest order term in the dividend $10 m$ by the highest order term in divisor $m$ .

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$5 m$

$10$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

$0 m$

$5 m^{2}$

$10 m$

$20$

Step 23

Multiply the new quotient term by the divisor.

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$5 m$

$10$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

$0 m$

$5 m^{2}$

$10 m$

$20$

$10 m$

$20$

Step 24

The expression needs to be subtracted from the dividend, so change all the signs in $10 m - 20$

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$5 m$

$10$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

$0 m$

$5 m^{2}$

$10 m$

$20$

$10 m$

$20$

Step 25

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

$m^{4}$

$2 m^{3}$

$4 m^{2}$

$5 m$

$10$

$m$

$2$

$m^{5}$

$0 m^{4}$

$0 m^{3}$

$3 m^{2}$

$0 m$

$20$

$m^{5}$

$2 m^{4}$

$0 m^{3}$

$2 m^{4}$

$4 m^{3}$

$3 m^{2}$

$4 m^{3}$

$8 m^{2}$

$5 m^{2}$

$0 m$

$5 m^{2}$

$10 m$

$20$

$10 m$

$20$

$0$

Step 26

Since the remander is $0$ , the final answer is the quotient.

$m^{4} + 2 m^{3} + 4 m^{2} + 5 m + 10$

Divide Using Long Polynomial Division (m^5-3m^2-20)÷(m-2)

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