Long division for polynomials involves dividing each term of the polynomial by the divisor, similar to long division with numbers. Here are the steps to solve (6x^4+30x^3+3x+14) / (x+):
1. Write the dividend and divisor in long division format, with the dividend on top and the divisor on the outside to the left.
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x+ |6x^4+30x^3+3x+14
2. Divide the first term of the dividend by the first term of the divisor, and write the quotient above the dividend.
6x^3
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x+ |6x^4+30x^3+3x+14
3. Multiply the divisor (x+) by the quotient (6x^3) and write the result underneath the first two terms of the dividend.
6x^3
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x+ |6x^4+30x^3+3x+14
6x^4+6x^3
4. Subtract the product from step 3 from the first two terms of the dividend, and bring down the next term of the dividend.
6x^3
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x+ |6x^4+30x^3+3x+14
6x^4+6x^3
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24x^3 + 3x
5. Repeat steps 2-4 with the new dividend (24x^3+3x).
6x^3 + 24x^2
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x+ |6x^4+30x^3+3x+14
6x^4+6x^3
_________
24x^3 + 3x
24x^3 + 24x^2
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-21x^2 + 3x
6. Repeat steps 2-4 with the new dividend (-21x^2+3x).
6x^3 + 24x^2 - 21x
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x+ |6x^4+30x^3+3x+14
6x^4+6x^3
_________
24x^3 + 3x
24x^3 + 24x^2
_____________
-21x^2 + 3x
-21x^2 - 21x
_____________
24
7. The quotient is 6x^3 + 24x^2 - 21x with a remainder of 24, written as:
6x^3 + 24x^2 - 21x + (24 / (x+))
How to solve (6x^4+30x^3+3x+14) / (x+) in long division. I understand synthetic but not long divison
1 answer