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Polynomials - Coggle Diagram
Polynomials
What is Polynomial: An algebraic expression is a collection of variables and real numbers. The most common type of algebraic expression is the polynomial.The "poly" in "polynomial" means "many". The term "polynomial" refers to sums of many terms, but the
term is used to refer to anything from one term to the sum of a zillion terms.
Sum of the coefficients of a polynomial is found by In order to find the sum of the coefficients of a
polynomial we substitute 1 for each variable.
The constant term of a polynomial is found by In order to find the constant term of a polynomial
we substitute zero for each variable.
Constant Polynomial:Constant polynomials are also called degree 0 polynomials. The graph of a constant polynomial is a horizontal line. A constant polynomial does not have any roots unless it is the polynomial P(x) = 0. EXAMPLE:P(x)=7
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an, an-1, ..., a2, a1, a0 are called coefficients of the polynomial.
The coefficient of term with the highest degree of x is called leading coefficients of the
polynomial.
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Zero Polynomial: If P(x)=0, it is called zero polynomial.Degree of zero polynomial is undetermined.
Equal Polynomial:Two polynomials are considered equal if they have equal coefficients of corresponding powers of the independent variable, after like terms are combined.
Adding and Subtracting PolynomialsThe 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.
Multiplication on Polynomials:To multiply one term by another term, first multiply the constants, then multiply each variable together and combine the result
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Division on Polynomials:Divide the term with the highest power inside the division symbol by the term with the highest power outside the division symbol.
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Factorization of Polynomials:The process of writing a polynomial as a product of two or more polynomials is called factoring.Let P(x), Q(x), and R(x) be polynomials. P(x) and Q(x) are called the factors of R(x) in the equation of
R(x) P(x).Q(x).
Factoring by Using Common Factor: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)]
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Factoring by Grouping:If there is no common number, common variable or common term in each term of a givenpolynomial, 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, thegroups are factor out any common factor.
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Factoring by Changing the Variable:It is the process of simplifying the polynomial by renaming similar terms with a new variable.
