Answer:
431
Step-by-step explanation:
Let
[tex]p(x) = {x}^{6} - 4 {x}^{4} + 4 {x}^{2} - 10[/tex]
We want to find the remainder when this polynomial is divided by x+3.
We use the remainder theorem.
Which says that, when p(x) is divided by x-a, the remainder is p(a)=R.
Therefore the remainder when p(x) is divided by x+3 is p(-3).
[tex]p( - 3) = {( - 3)}^{6} - 4 { (- 3)}^{4} + 4 {( - 3)}^{2} - 10[/tex]
We evaluate:
[tex]p( - 3) = 729 - 4 (81)+ 4 {( 9)} - 10[/tex]
We multiply to get;
[tex]p( - 3) = 729 - 324+ 36- 10[/tex]
We simplify to get:
[tex]p( - 3) =431[/tex]
Therefore the remainder is 431
