Find the Quotient (4t^7)/(2t)

$\frac{4 t^{7}}{2 t}$

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

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

Divide the highest order term in the dividend $4 t^{7}$ by the highest order term in divisor $2 t$ .

$2 t^{6}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

Multiply the new quotient term by the divisor.

$2 t^{6}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

The expression needs to be subtracted from the dividend, so change all the signs in $4 t^{7} + 0$

$2 t^{6}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

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

$2 t^{6}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

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

$2 t^{6}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

Divide the highest order term in the dividend $0 t^{5}$ by the highest order term in divisor $2 t$ .

$2 t^{6}$

$0 t^{5}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

Multiply the new quotient term by the divisor.

$2 t^{6}$

$0 t^{5}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

$0$

The expression needs to be subtracted from the dividend, so change all the signs in $0 + 0$

$2 t^{6}$

$0 t^{5}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

$0$

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

$2 t^{6}$

$0 t^{5}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

$0$

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

$2 t^{6}$

$0 t^{5}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

$0$

$0 t^{3}$

$0 t^{2}$

Divide the highest order term in the dividend $0 t^{3}$ by the highest order term in divisor $2 t$ .

$2 t^{6}$

$0 t^{5}$

$0 t^{3}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

$0$

$0 t^{3}$

$0 t^{2}$

Multiply the new quotient term by the divisor.

$2 t^{6}$

$0 t^{5}$

$0 t^{3}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

$0$

$0 t^{3}$

$0 t^{2}$

$0$

The expression needs to be subtracted from the dividend, so change all the signs in $0 + 0$

$2 t^{6}$

$0 t^{5}$

$0 t^{3}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

$0$

$0 t^{3}$

$0 t^{2}$

$0$

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

$2 t^{6}$

$0 t^{5}$

$0 t^{3}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

$0$

$0 t^{3}$

$0 t^{2}$

$0$

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

$2 t^{6}$

$0 t^{5}$

$0 t^{3}$

$2 t$

$0$

$4 t^{7}$

$0 t^{6}$

$0 t^{5}$

$0 t^{4}$

$0 t^{3}$

$0 t^{2}$

$0 t$

$0$

$4 t^{7}$

$0$

$0 t^{5}$

$0 t^{4}$

$0$

$0 t^{3}$

$0 t^{2}$

$0$

$0 t$

$0$

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

$2 t^{6} + 0 t^{5} + 0 t^{3}$

Find the Quotient (4t^7)/(2t)

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