Divisor of Polynomial/Examples/Arbitrary Example 1

Examples of Divisors of Polynomials

The expressions:

$x - 1$

$x + 2$

are divisors of the polynomial $x^2 + x - 2$

Proof

We have:

\(\ds \paren {x - 1} \paren {x + 2}\)

\(=\)

\(\ds x \paren {x + 2} + \paren {-1} \paren {x + 2}\)

Distributive Laws of Arithmetic

\(\ds \)

\(=\)

\(\ds \paren {x^2 + 2 x} + \paren {-x - 2}\)

Distributive Laws of Arithmetic

\(\ds \)

\(=\)

\(\ds x^2 + x - 2\)

simplifying

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): factor
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): factor: 1.