Double Synthetic Division: Dividing a Polynomial by a Trinomial

A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient.  The simplest polynomials have one variable. 

Polynomials in one variable are algebraic expressions that consist of terms in the form axn where n is a non-negative (i.e. positive or zero) integer and a is a real number and is called the coefficient of the term.  The degree of a polynomial in one variable is the largest exponent in the polynomial.

Note that we will often drop the “in one variable” part and just say polynomial.

Here are examples of polynomials and their degrees.

There are two cases for dividing polynomials: either the "division" is really just a simplification and you're just reducing a fraction or else you need to do long polynomial division. However, synthetic division is a shorthand, or shortcut, method of polynomial division (long method of division) in the special case of dividing by a linear factor. Here is an example.

 -- and it only works in this case. Or so we thought?

What if you are asked to divide a polynomial in one variable and it isn't by a linear factor, but by a TRINOMIAL where the leading coefficient can either be 1 or not? Are you still up for that challenge? Before you say no, here's a MATHEMATIP by the name of DOUBLE SYNTHETIC DIVISION. Remember, ESCAPE THE COMPLEX.

DIVIDING A POLYNOMIAL BY A TRINOMIAL USING SYNTHETIC DIVISION (a = 1)

If the video cannot be viewed, kindly click the link below:
https://www.youtube.com/watch?v=mdgWnxohHNg

DIVIDING A POLYNOMIAL BY A TRINOMIAL USING SYNTHETIC DIVISION (a is not 1)

If the video cannot be viewed, kindly click the link below:
https://www.youtube.com/watch?v=T7YOSJcNXfE