“Polynomial” comes from the word ‘Poly’ (Meaning Many) and ‘nomial’ (in this case meaning Term)-so it means many terms. A polynomial is made up of terms that are only added, subtracted or multiplied. A quadratic polynomial in x with real coefficients is of the form ax² + bx + c, where a, b, c are real numbers with a ≠ 0. A polynomial can have terms which have Constants like 3, -20, etc., Variables like x and y and Exponents like 2 in y². These can be combined using addition, subtraction and multiplication but NOT DIVISION.
Types Of Polynomials
Polynomials can be classified based on:
a) Number of terms
b) Degree of the polynomial.
Types of polynomials based on the number of terms
Types of Polynomials based on Degree
A polynomial whose degree is one is called a linear polynomial.
For example, 2x+1 is a linear polynomial.
A polynomial of degree two is called a quadratic polynomial.
For example, 3x2+8x+5 is a quadratic polynomial.
A polynomial of degree three is called a cubic polynomial.
For example, 2x3+5x2+9x+15 is a cubic polynomial.
Now, let us take an example and see how we can do the factorization of a polynomial using area method
Multiplying (x + 2) by (x + 3) can be represented like so in the figure. This makes the following operations look rather simple:
(x + 2)( x + 3)
x 2 + 2x + 3x + 6
x2 + 5x + 6
Using the area method for multiplying binomials also makes factoring an easy task. We can visualize the squares and rectangles in this shape while thinking to ourselves, “Which two numbers have a sum of 5 (second term) and a product of 6 (third term)?”