Question

P(x) = 2x4+6x3-5x-10; (x+2)
Determine if it’s a factor

Answer 1

I have put the full working using remainder theorem to prove that x+2 isn’t a factor

Answer 2

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

`p( - 2) = 2 ({ - 2})^(4) + 6( { - 2})^(3) - 5( - 2) - 10 \\ = 2(16) + 6( - 8) + 10 - 10 \\ = 32 - 48 \\ = - 16`

Since it leaves a remainder of - 16 (x + 2) is not a factor of the polynomial

Hope this helps you