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Polynomials - Coggle Diagram
Polynomials
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Definition
where a_0,a_1,a_2, . . . ,a_n are constants and a_n is not equal to 0
A polynomial p(x) in one variable x is an algebraic expressionin x of the form
p(x) = *a_nx^n + a_n-1x^n-1 + . . . + a_2x^2 + a_1x + a_0
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Remainder theorem
Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a). ... Solution: Zero of x – 1 is 1, so as per remainder theorem remainder in this case will be p(1) .
Factor Theorem
In mathematics, factor theorem is used when factoring the polynomials completely. It is a theorem that links factors and zeros of the polynomial. According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.
Coefficients
coefficient is an integer that is written along with a variable or it is multiplied by the variable. In other words, a coefficient is the numerical factor of a term containing constant and variables. For example, in the term 2x, 2 is the coefficient.