Divide (x^4-x^3-14x^2+7x-4)/(x-4)

Math
x4-x3-14×2+7x-4x-4
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
x4x4x314×2+7x4
Divide the highest order term in the dividend x4 by the highest order term in divisor x.
x3
x4x4x314×2+7x4
Multiply the new quotient term by the divisor.
x3
x4x4x314×2+7x4
+x44×3
The expression needs to be subtracted from the dividend, so change all the signs in x4-4×3
x3
x4x4x314×2+7x4
x4+4×3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x3
x4x4x314×2+7x4
x4+4×3
+3×3
Pull the next terms from the original dividend down into the current dividend.
x3
x4x4x314×2+7x4
x4+4×3
+3×314×2
Divide the highest order term in the dividend 3×3 by the highest order term in divisor x.
x3+3×2
x4x4x314×2+7x4
x4+4×3
+3×314×2
Multiply the new quotient term by the divisor.
x3+3×2
x4x4x314×2+7x4
x4+4×3
+3×314×2
+3×312×2
The expression needs to be subtracted from the dividend, so change all the signs in 3×3-12×2
x3+3×2
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x3+3×2
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2
Pull the next terms from the original dividend down into the current dividend.
x3+3×2
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2+7x
Divide the highest order term in the dividend -2×2 by the highest order term in divisor x.
x3+3×22x
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2+7x
Multiply the new quotient term by the divisor.
x3+3×22x
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2+7x
2×2+8x
The expression needs to be subtracted from the dividend, so change all the signs in -2×2+8x
x3+3×22x
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2+7x
+2×28x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x3+3×22x
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2+7x
+2×28x
x
Pull the next terms from the original dividend down into the current dividend.
x3+3×22x
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2+7x
+2×28x
x4
Divide the highest order term in the dividend -x by the highest order term in divisor x.
x3+3×22x1
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2+7x
+2×28x
x4
Multiply the new quotient term by the divisor.
x3+3×22x1
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2+7x
+2×28x
x4
x+4
The expression needs to be subtracted from the dividend, so change all the signs in -x+4
x3+3×22x1
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2+7x
+2×28x
x4
+x4
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x3+3×22x1
x4x4x314×2+7x4
x4+4×3
+3×314×2
3×3+12×2
2×2+7x
+2×28x
x4
+x4
8
The final answer is the quotient plus the remainder over the divisor.
x3+3×2-2x-1-8x-4
Divide (x^4-x^3-14x^2+7x-4)/(x-4)

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