Is x^2 + bx + ax + ab a quadratic trinomial?

Question

Quadratic trinomials are obtained when binomial expressions are expanded. Consider the following:

(x + a)(x + b) = x² + bx + ax + ab

 

This means that quadratic trinomials of the form x² + (a + b) x + ab when factorized will give (x + a)(x + b)

 

doesnt a trinomial only have 3 terms? i.e. x² + 3x + 2

Answer 1

x² + bx + ax + ab is a quadratic and it does have only three terms.  The terms ax and bx are like-terms that can be combined into (a+b)x which changes the equation into the form x² + (a + b) x + ab.  Remember, a and b are just numbers.  For example let a = 1 and b = 2:

 

x² + (a + b) x + ab

x² + (1+2)x + (1)(2)

x² + 3x + 2

 

The point is that the coefficient of the x term is equal to the sum of two number (a+b) while the constant term is equal to the product (ab) of the same two numbers.  That fact allows you factor quadratics into (x+a)(x+b).