What is a comosite polynomial? What is special about perfect square trinomials and differences of two squares?

Answer 1

A composite polynomial is one which is the product of two factors of lower degree. For polynomials over the complex numbers with complex coefficients, this is every polynomial of degree two or higher (cf. Fundamental Theorem of Algebra).

The nice thing about perfect square trinomials and differences of squares is that both of them have particularly simple factorizations.

Answer 2

Polynomial composition involves replacing the variable x in a polynomial with another polynomial.
For example,
P(Q(x)) = a0 + a1Q(x) + a2(Q(x))^2 + a3(Q(x))^3
P(Q(x)) denotes the composite polynomial.

Perfect square trinomial is the square of a binomial
example: (ax + b) ^2 = a^2x^2 + 2abx + b^2

Diffrence of two squares has special properties in that their factors are the sum and difference of the unsquared terms.
example: x^2 - a^2 = (x+a)(x-a)