ANSWER
The remainder is
[tex]60[/tex]
EXPLANATION
Let
[tex]p(x) = 5 {x}^{2} + 10x - 15[/tex]
We shall apply the remainder theorem to obtain the remainder when
[tex]p(x)[/tex]
is divided by
[tex]x + 5[/tex]
According to the remainder theorem, if a polynomial
[tex]p(x)[/tex]
is divided by
[tex]x - a[/tex]
then the remainder is
[tex]p(a)[/tex]
So we set
[tex]x + 5 = 0[/tex]
and solve for
[tex]x[/tex]
to obtain,
[tex]x = - 5[/tex]
We now substitute -5 into the given polynomial to find the remainder.
[tex]p( - 5) = 5 {( - 5)}^{2} + 10( - 5) - 15[/tex]
This gives us,
[tex]p( - 5) = 5(25) - 50 - 15[/tex]
This will simplify to,
[tex]p( - 5) = 125 - 50 - 15[/tex]
[tex]p( - 5) = 60[/tex]
Therefore the remainder is
[tex]60[/tex]
