Answer
true
Work Step by Step
The fist row of the synthetic division shows $c$ and the coefficients of the dividend in descending order of degree.
Thus, the synthetic division involves:
$c=-2$ which means the divisor $x-c$ is $x-(-2) = x+2$
dividend = $5x^3+3x^2+x+1$
The last row of the synthetic division shows the quotient, with the degree of each term one lower than the dividend.
The rightmost entry is the remainder.
Thus, the quotient is $5x^2-7x+16$ with a remainder of $-31$.
Therefore, the division and the quotient can be written as:
$\dfrac{5x^3+3x^2+x+1}{x+2}=5x^2-7x+16+\dfrac{-31}{x+2}$
The given statement is true.
