Question

I want to know the correct equation by the synthetic division problem

Answer 1

When using synthetic division the numbers on top represent the coefficients of the polynomial that represents the dividend. The coefficients are arranged in descending order of exponents, therefore, the dividend of the synthetic division shown is:

`x^3+8x^2+14x-8`

In the synthetic division, the number on the left is the root of the divisor, therefore, we have:

`\begin{gathered} x=-4 \\ x+4=0 \end{gathered}`

Therefore, the divisor is "x + 4".

Finally, the numbers at the bottom are the coefficient of the result of the division but we subtract 1 from the exponents of the polynomial. We write each of the coefficients with its corresponding polynomial from left to right and the last number is the remainder of the division, therefore, we have that the result is:

`x^2+4x-2`

Therefore, the correct equation is:

`(x^3+8x^2+14x-8)/(x-4)=x^2+4x-2`