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How to Factor Cubic Polynomials?

TopCubic Polynomials are basically those in which the highest degree of the polynomial is 3 of the form ap3 + bp2 + cp + d. For Example: (44 q3 + 37q – 2). To understand how to factor cubic polynomials we need to follow certain steps which are given as: Considering an example: (21h3 + 35h2). To factorize it first identify each term present in the polynomial, then go for finding the common factors in each term.
3 * 7 * h* h * h + 5 * 7 * h * h
Here in our example we have 7h2 as the common term. It is also called as the greatest common factor (GCF) in all the term of the polynomial. Here,
GCF (7h2) = 7h2
Use the distributive property: [a (b + c) = ab + ac] to take out the GCF from the polynomial and thus reducing it further:
21h3 + 35h2 = 7h2 (3h + 5)
In case we have a polynomial of type: 21h3 - 35h2 + 14h. We need to solve those polynomials also (if possible) which are generated during the Factorization. In the second polynomial that we have considered the GCF or the common factor is coming out to be 7h,
3 * 7 * h* h * h - 5 * 7 * h * h + 2 * 7 * h
Taking out the common factor from the above polynomial gives us:
21h3 - 35h2 + 14h = 7h2 (3h2 - 5h + 2)
(3h2 - 5h + 2) can further be factorized as (h -1) (3h – 2). So our final result after factorization would be:
21h3 - 35h2 + 14h = 7h2 (3h2 - 5h + 2) = 7h2 (h -1) (3h – 2)
The polynomials can also be factorized using the hit and trial method, where we check for what all values of ‘h’ the polynomial results to zero. But this approach is valid only for the polynomials with fewer complications.