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:fire:POLYNOMIALS :fire:, Adding and Subtracting Polynomials,…
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POLYNOMIALS
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An algebraic expression is a collection of variables and real numbers. The most common type of
algebraic expression is the polynomial.
The Algebraic Operations on Polynomials
Let P(x) and Q(x) be two polynomials. By doing multiplication of P(x).Q(x), each terms of P(x) are multiplied with each terms of Q(x) and addition of these algebraic expressions is written in descending or ascending powers of the variable x from the beginning.
For the polynomials P(x), Q(X) ≠ 0 and deg[P(x)] ≥ deg[Q(x)] ≥ 1, the division of P(x) with Q(x) is shown in the following way
The sum of two polynomials is obtained by
adding together the coefficients sharing the
same powers of the variable
The difference of two polynomials is obtained by subtracting together the coefficients sharing the
same powers of the variable.
Factorization of Polynomials
The first step in completely factoring a polynomial is to remove (factor out) any
common factors.
For the polynomials A(x), B(x), and C(x),
A(x).B(x) A(x).C(x) A(x).[B(x) C(x)]
The process of writing a polynomial as a product of two or more polynomials is called factoring.
It is the process of simplifying the polynomial by renaming similar terms with a new variable.
If there is no common number, common variable or common term in each term of a given polynomial, the terms that have any common factors are made a group by coming together. Then, each group are factor out such that they have the same expression in parentheses. After that, the groups are factor out any common factor.
Adding and Subtracting Polynomials
Multiplication on Polynomials
Division on Polynomials
Factoring by Using Common Factor
Factoring by Grouping
Factoring by Identities
Perfect Square
Difference of Two Square
Factoring the Cube of Sum and Difference
Factoring the Sum and Difference of Two Cube
Factoring Three Terms Polynomial
Factoring by Changing the Variable
