Taking p(x) = 2x² + 3x + 5, q(x) = x² + 4x + 1 and s(x) = p(x) + q(x), calculate p(10), q(10), s(10), p(10) + q(10).

(i) p(10)

p(x) = 2x² + 3x + 5

p(10) = 2(10)² + 3(10) + 5

p(10) = 235 – (1)

(ii) q(10)

q(x) = x² + 4x + 1

q(10) = (10)² + 4(10) + 1

q(10) = 141 – (1)

(iii) s(x) = p(x) + q(x)

s(x) = 2x² + 3x + 5 + x² + 4x + 1

s(x) = 3x² + 7x + 6

s(10) = 3(10)² + 7(10) + 6

s(10) = 376

(iv) p(10) + q(10)

by (1) and (2)

p(10) + q(10) = 235 + 141

p(10) + q(10) = 376

This is the same result as (iii)

⇒ Polynomials have Commutative Property of Addition.