Divide Using Synthetic Division (12x^4+5x^3+3x^2-5)/(x+1)

Problem

(12*x4+5*x3+3*x2−5)÷(x+1)

Solution

1. Identify the coefficients of the dividend and the zero of the divisor. The dividend is 12*x4+5*x3+3*x2+0*x−5 (including the placeholder for x, so the coefficients are 12, 5, 3, 0, -5.T*h*e*d(i)*v*i*s(o)*r*i*s() + 1,s(o)*t*h*e*z*e*r*o*i*s() = -1$.

2. Set up the synthetic division by bringing down the leading coefficient 12

3. Multiply the zero −1 by the current value 12 to get −12 place it under the next coefficient 5 and add to get −7

4. Multiply the zero −1 by −7 to get 7 place it under the next coefficient 3 and add to get 10

5. Multiply the zero −1 by 10 to get −10 place it under the next coefficient 0 and add to get −10

6. Multiply the zero −1 by −10 to get 10 place it under the last coefficient −5 and add to get the remainder 5

7. Interpret the resulting coefficients 12, -7, 10, -10$ as the coefficients of the quotient, which will be one degree lower than the dividend.

Final Answer

(12*x4+5*x3+3*x2−5)÷(x+1)=12*x3−7*x2+10*x−10+5/(x+1)

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