Polynomials, Perfect Square, Differences in Squares and Cubes
Introduction
So more stuff I probably know but here because I struggle with words.
Terms
These are mathematical expressions with consist of a Number and a variable for example 2x. The number part is called the coefficient which is a fancy way of saying the number you need to multiply by. The variable part can be a name and raised by a power.
Polynomial
A polynomial is a combination of many terms. e.g 2x²+3x+24. Each term must be joined by addition or subtraction not multiplication other binary operators. There are names for terms
- 1 term - monomial
- 2 terms - binomial
- 3 terms - trinomial
- More than 3 - polynomial
Examples
So some polynomial may not show the number or the variable part. For example
3x² + x -5
All this means is we have abbreviated the expression.
3x² + 1x -5x⁰
There now it looks proper. The last term which is just a number is known as the constant term as it never changes.
Degree of a term
The degree of a term is determined by the power of the variable part so given 2x²+3x+24
- 2x² 2nd degree term
- 3x 1st degree term
- 24 constant term
Where there are 2 variable we add them together 8x²y³ is a 5 degree term
People refer to the whole polynomial by the highest degree to 2x²+3x+24. So this is a 2nd degree polynomial. Polynomials are arranged by degree.
Simplifying Polynomials
So like terms can be added together
2x³+2x²+5x²+10
Can be
2x³+7²x+10
Long Division
So getting more tricky below we need to follow a process. The question is
(x² + 5x + 6) / (x + 2)
So we put the denominator on the left like normal long division
----------------------------- (x + 2) | x² + 5x + 6