Given:
A polynomial has a root of −2.
To find:
The factor that will divide evenly into the polynomial.
Solution:
We know that, if c is a root of a polynomial P(x), then (x-c) is a factor of polynomial P(x).
we have,
-2 is a root of polynomial.
⇒ (x-(-2)) is a factor of polynomial.
⇒ (x+2) is a factor of polynomial.
⇒ (x+2) will divide the polynomial completely.
Therefore, the factor (x+2) will divide evenly into the polynomial.
The factors of a polynomial divide the polynomial evenly, without remainder
The factor of the polynomial is x + 2
The root of the polynomial is given as:
[tex]\mathbf{Root = -2}[/tex]
Assume the polynomial is a function of x.
i.e. the variable of the polynomial is x
Then the root can be represented as:
[tex]\mathbf{x= -2}[/tex]
Add 2 to both sides
[tex]\mathbf{x + 2= -2 +2}[/tex]
So, we have:
[tex]\mathbf{x + 2= 0}[/tex]
Hence, the factor of the polynomial is x + 2
Read more about polynomial factors at:
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