Divide (12x^4+17x^3+8x-40)÷(x+2)

Math
(12×4+17×3+8x-40)÷(x+2)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
x+212×4+17×3+0x2+8x40
Divide the highest order term in the dividend 12×4 by the highest order term in divisor x.
12×3
x+212×4+17×3+0x2+8x40
Multiply the new quotient term by the divisor.
12×3
x+212×4+17×3+0x2+8x40
+12×4+24×3
The expression needs to be subtracted from the dividend, so change all the signs in 12×4+24×3
12×3
x+212×4+17×3+0x2+8x40
12×424×3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
12×3
x+212×4+17×3+0x2+8x40
12×424×3
7×3
Pull the next terms from the original dividend down into the current dividend.
12×3
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
Divide the highest order term in the dividend -7×3 by the highest order term in divisor x.
12×37×2
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
Multiply the new quotient term by the divisor.
12×37×2
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
7×314×2
The expression needs to be subtracted from the dividend, so change all the signs in -7×3-14×2
12×37×2
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
12×37×2
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2
Pull the next terms from the original dividend down into the current dividend.
12×37×2
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2+8x
Divide the highest order term in the dividend 14×2 by the highest order term in divisor x.
12×37×2+14x
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2+8x
Multiply the new quotient term by the divisor.
12×37×2+14x
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2+8x
+14×2+28x
The expression needs to be subtracted from the dividend, so change all the signs in 14×2+28x
12×37×2+14x
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2+8x
14×228x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
12×37×2+14x
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2+8x
14×228x
20x
Pull the next terms from the original dividend down into the current dividend.
12×37×2+14x
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2+8x
14×228x
20x40
Divide the highest order term in the dividend -20x by the highest order term in divisor x.
12×37×2+14x20
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2+8x
14×228x
20x40
Multiply the new quotient term by the divisor.
12×37×2+14x20
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2+8x
14×228x
20x40
20x40
The expression needs to be subtracted from the dividend, so change all the signs in -20x-40
12×37×2+14x20
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2+8x
14×228x
20x40
+20x+40
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
12×37×2+14x20
x+212×4+17×3+0x2+8x40
12×424×3
7×3+0x2
+7×3+14×2
+14×2+8x
14×228x
20x40
+20x+40
0
Since the remander is 0, the final answer is the quotient.
12×3-7×2+14x-20
Divide (12x^4+17x^3+8x-40)÷(x+2)

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