Step-by-step explanation:
Using the remainder theorem when , when the value of x + 2 is substituted into the polynomial if it's a factor it will produce a result of zero else any number will prove that it's not a factor.
So we have
x + 2 = 0
x = - 2
Substitute the value of x into the polynomial
That's
[tex]p( - 2) = 2 ({ - 2})^{4} + 6( { - 2})^{3} - 5( - 2) - 10 \\ = 2(16) + 6( - 8) + 10 - 10 \\ = 32 - 48 \\ = - 16[/tex]
Since it leaves a remainder of - 16 (x + 2) is not a factor of the polynomial
Hope this helps you
