Answer:
The remainder is 55
Step-by-step explanation:
Let
[tex]p(x)= 2 {x}^{4} + {x}^{2} - 10x - 1[/tex]
According to the remainder theorem, if p(x) is divided by x+a, the remainder is p (-a).
The given divisor is x+2, therefore the remainder is given by:
[tex]p( - 2)[/tex]
We substitute x=-2 to get:
[tex]p( - 2)= 2 {( - 2)}^{4} + {( - 2)}^{2} - 10( - 2) - 1[/tex]
We simplify to obtain:
[tex]p( - 2)= 2 \times 16 + 4 + 20- 1[/tex]
We multiply to get:
[tex]p( - 2)=3 2 + 4 + 20- 1 = 55[/tex]
Therefore the remainder is 55
