TopPolynomial is a mathematical equation or expression which consists of variables and constants. Operations which take place in Polynomials are usually addition, subtraction, multiplication. Division with a variable is not allowed in construction of polynomials but it can be performed using constants. As a2 − a/6 + 9 is a polynomial. Lets understand polynomial by following equation 5a2 - 6a + 10.
In above equation, first term is of degree 2, second term is of degree 1 and degree of third term is 0. This is called as polynomial. If degree is 4 then it will be called as polynomial of degree 4. Fourth degree polynomial consists of several single variable terms of variable degrees along with numerical coefficients and constants. In Factorization of fourth degree polynomials, result may contain four distinct zeros or roots.
A polynomial has n th power and will be represented by (A - B)n.
If n = 4 then it is called as polynomial of fourth power or degree four.
Let’s try to understand how to factor polynomials of degree 4 by taking following example a4 – b4.
Term a4 can be written as (a2)2 and similarly b4 can be written as (b2)2. Then we can write
a4 – b4 = (a2)2 - (b2)2,
Above equation is in binomial form, now simply factor it into two binomials. Among these two binomials, one will contain plus sign and other will have negative sign as shown below.
(a2 + b2) (a2 - b2),
Second term again can be factorized as per rules for binomials,
(a2 - b2) = (a + b) (a – b),
Then finally solution for polynomial of degree four can be given as:
a4 – b4 = (a2 + b2) (a + b) (a – b).