Polynomial Addition/Examples/Arbitrary Example 1

Example of Polynomial Addition

Let:

\(\ds P_1\)

\(=\)

\(\ds x^2 + 2 x + 3\)

\(\ds P_2\)

\(=\)

\(\ds 2 x^2 + x + 5\)

Then:

$P_1 + P_2 = 3 x^2 + 3 x + 8$

Proof

\(\ds P_1 + P_2\)

\(=\)

\(\ds \paren {x^2 + 2 x + 3} + \paren {2 x^2 + x + 5}\)

by hypothesis

\(\ds \)

\(=\)

\(\ds \paren {x^2 + 2 x^2} + \paren {2 x + x} + \paren {3 + 5}\)

Definition of Polynomial Addition

\(\ds \)

\(=\)

\(\ds 3 x^2 + 3 x + 8\)

$\blacksquare$

Sources

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