How do you determine whether x+2 is a factor of the polynomial #5x^2+2x+6#?
You see if
Let's suppose you have this factorized polynomial:
A property of this factorized polynomial is that each of it's factors when set to 0 is the root to this polynomial.
For example, when
This property arises from the property in which when
Now, back to your polynomial. Let's set it to 0 first and solve for
Using the quadratic formula, we get
Use the remainder theorem to find
Given a polynomial
In our example:
#f(x) = 5x^2+2x+6#
#f(-2) = 5(color(blue)(-2))^2+2(color(blue)(-2))+6#
#color(white)(f(-2)) = 20-4+6#
#color(white)(f(-2)) = 22#
Since this is not zero,