ANSWER
The remainder is 15.
EXPLANATION
The given polynomial function is
\(p(x) = 3 {x}^{4} + 2 {x}^{3} - {x}^{2} + 2x - 9\)
We want to find the remainder when the given polynomial function is divided by
\(x + 2\)
According to the Remainder Theorem, if
\(p(x) = 3 {x}^{4} + 2 {x}^{3} - {x}^{2} + 2x - 9\)
is divided by
\(x + 2\)
Then the remainder is
\(p( - 2)\)
This means that, we have to substitute
\(x = - 2\)
into the given polynomial function and evaluate.
Thus,
\(p( - 2) = 3 {( - 2)}^{4} + 2 {( - 2)}^{3} - {( - 2)}^{2} + 2( - 2)- 9\)
\(p( - 2) = 3 {( 16)} + 2 {( - 8)} - {( 4)} + 2( - 2)- 9\)
\(p( - 2) = 48 - 16- 4 - 4- 9\)
\(p( - 2) = 15\)
Therefore the remainder is 15
