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:

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

$\ds P_1 + P_2$

$=$

$\ds \paren {x^2 + 2 x + 3} + \paren {2 x^2 + x + 5}$

by hypothesis

$\ds $

$=$

$\ds \paren {x^2 + 2 x^2} + \paren {2 x + x} + \paren {3 + 5}$

Definition of Polynomial Addition

$\ds $

$=$

$\ds 3 x^2 + 3 x + 8$

$\blacksquare$

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