Recall:
(a + b) (2a + 3b) = 2a2 + 3ab + 2ab + 3b2
= 2a2 + 5ab + 3b2
As seen above, multiplication of two polynomials are done similar. Multiplying all terms and adding similar power terms together.
Example; given that
P(x) = 2x3 + 3x2 – 2x + 1 , h(x) = (2x + 3), find; h(x) × p(x)
Solution
h(x) × p(x) = (2x + 3) (2x3 + 3x2 – 2x + 1)
= (4x4 + 6x3 – 4x2 + 2x) + (6x3 + 9x2 – 6x + 3)
= 4x4 + 12x3 + 5x2 – 4x + 3
