Strategy #13: Connect Polynomial Roots to Factors

Category: Advanced Math

If r is a root (zero) of a polynomial, then (x − r) is a factor. Conversely, if (x − r) is a factor, then r is a root. And if our factor is written instead as (r – x), r will still be a root.

Why it matters: The SAT will ask you to identify roots from a factored form, write a polynomial given its roots, or determine how many times the graph crosses the x-axis.

Key facts:

• A root where the factor appears once → graph crosses the x-axis

• A root where the factor appears twice (repeated root) → graph touches but does not cross the x-axis

Practice tip: Given a polynomial in factored form, set each factor equal to zero to find the roots instantly.

Try this example: