Find the Quotient (x^5+x^3-x^2)÷(x-4)

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

Step 1

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

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

Step 2

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

$x^{4}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

Step 3

Multiply the new quotient term by the divisor.

$x^{4}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

Step 4

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

$x^{4}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

Step 5

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

$x^{4}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

Step 6

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

$x^{4}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

Step 7

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

$x^{4}$

$4 x^{3}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

Step 8

Multiply the new quotient term by the divisor.

$x^{4}$

$4 x^{3}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $4 x^{4} - 16 x^{3}$

$x^{4}$

$4 x^{3}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

Step 10

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

$x^{4}$

$4 x^{3}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

Step 11

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

$x^{4}$

$4 x^{3}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

Step 12

Divide the highest order term in the dividend $17 x^{3}$ by the highest order term in divisor $x$ .

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

Step 13

Multiply the new quotient term by the divisor.

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $17 x^{3} - 68 x^{2}$

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

Step 15

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

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

Step 16

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

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

$0 x$

Step 17

Divide the highest order term in the dividend $67 x^{2}$ by the highest order term in divisor $x$ .

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$67 x$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

$0 x$

Step 18

Multiply the new quotient term by the divisor.

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$67 x$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

$0 x$

$67 x^{2}$

$268 x$

Step 19

The expression needs to be subtracted from the dividend, so change all the signs in $67 x^{2} - 268 x$

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$67 x$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

$0 x$

$67 x^{2}$

$268 x$

Step 20

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

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$67 x$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

$0 x$

$67 x^{2}$

$268 x$

Step 21

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

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$67 x$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

$0 x$

$67 x^{2}$

$268 x$

$0$

Step 22

Divide the highest order term in the dividend $268 x$ by the highest order term in divisor $x$ .

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$67 x$

$268$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

$0 x$

$67 x^{2}$

$268 x$

$0$

Step 23

Multiply the new quotient term by the divisor.

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$67 x$

$268$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

$0 x$

$67 x^{2}$

$268 x$

$0$

$268 x$

$1072$

Step 24

The expression needs to be subtracted from the dividend, so change all the signs in $268 x - 1072$

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$67 x$

$268$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

$0 x$

$67 x^{2}$

$268 x$

$0$

$268 x$

$1072$

Step 25

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

$x^{4}$

$4 x^{3}$

$17 x^{2}$

$67 x$

$268$

$x$

$4$

$x^{5}$

$0 x^{4}$

$x^{3}$

$x^{2}$

$0 x$

$0$

$x^{5}$

$4 x^{4}$

$x^{3}$

$4 x^{4}$

$16 x^{3}$

$17 x^{3}$

$x^{2}$

$17 x^{3}$

$68 x^{2}$

$67 x^{2}$

$0 x$

$67 x^{2}$

$268 x$

$0$

$268 x$

$1072$

Step 26

The quotient is $x^{4} + 4 x^{3} + 17 x^{2} + 67 x + 268$ .

$x^{4} + 4 x^{3} + 17 x^{2} + 67 x + 268$

Find the Quotient (x^5+x^3-x^2)÷(x-4)

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