Algebra Examples

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Algebra
Find the Remainder (4x^15-6x^2-5x+6)/(x-1)
Step 1
To calculate the remainder, first divide the polynomials.
Tap for more steps...
Step 1.1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
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Step 1.2
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.3
Multiply the new quotient term by the divisor.
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Step 1.4
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.5
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.6
Pull the next terms from the original dividend down into the current dividend.
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Step 1.7
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.8
Multiply the new quotient term by the divisor.
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Step 1.9
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.10
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.11
Pull the next terms from the original dividend down into the current dividend.
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Step 1.12
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.13
Multiply the new quotient term by the divisor.
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Step 1.14
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.15
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.16
Pull the next terms from the original dividend down into the current dividend.
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Step 1.17
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.18
Multiply the new quotient term by the divisor.
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Step 1.19
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.20
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.21
Pull the next terms from the original dividend down into the current dividend.
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Step 1.22
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.23
Multiply the new quotient term by the divisor.
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Step 1.24
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.25
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.26
Pull the next terms from the original dividend down into the current dividend.
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Step 1.27
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.28
Multiply the new quotient term by the divisor.
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Step 1.29
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.30
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.31
Pull the next terms from the original dividend down into the current dividend.
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Step 1.32
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.33
Multiply the new quotient term by the divisor.
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Step 1.34
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.35
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.36
Pull the next terms from the original dividend down into the current dividend.
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Step 1.37
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.38
Multiply the new quotient term by the divisor.
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Step 1.39
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.40
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.41
Pull the next terms from the original dividend down into the current dividend.
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Step 1.42
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.43
Multiply the new quotient term by the divisor.
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Step 1.44
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.45
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.46
Pull the next terms from the original dividend down into the current dividend.
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Step 1.47
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.48
Multiply the new quotient term by the divisor.
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Step 1.49
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.50
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.51
Pull the next terms from the original dividend down into the current dividend.
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Step 1.52
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.53
Multiply the new quotient term by the divisor.
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Step 1.54
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.55
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.56
Pull the next terms from the original dividend down into the current dividend.
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Step 1.57
Divide the highest order term in the dividend by the highest order term in divisor .
+++++++++++
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Step 1.58
Multiply the new quotient term by the divisor.
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Step 1.59
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.60
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.61
Pull the next terms from the original dividend down into the current dividend.
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Step 1.62
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.63
Multiply the new quotient term by the divisor.
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Step 1.64
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.65
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.66
Pull the next terms from the original dividend down into the current dividend.
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Step 1.67
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.68
Multiply the new quotient term by the divisor.
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Step 1.69
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.70
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.71
Pull the next terms from the original dividend down into the current dividend.
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Step 1.72
Divide the highest order term in the dividend by the highest order term in divisor .
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Step 1.73
Multiply the new quotient term by the divisor.
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Step 1.74
The expression needs to be subtracted from the dividend, so change all the signs in
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Step 1.75
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
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Step 1.76
The final answer is the quotient plus the remainder over the divisor.
Step 2
Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.