5 is polynomial or not?
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(Yes, "5" is a polynomial, one term is allowed, and it can be just a constant!) 3xy-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)
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Remember that a polynomial is any algebraic expression that consists of terms in the form axn a x n . Another way to write the last example is. −8x0. Written in this way makes it clear that the exponent on the x is a zero (this also explains the degree…) and so we can see that it really is a polynomial in one variable.
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Answer. Let us assume that √5 is a rational number. we know that the rational numbers are in the form of p/q form where p,q are intezers. hence our assumption is wrong and √5 is an irrational number.
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If α and β are zeroes of a quadratic polynomial p(x), then factorize p(x)? thus P(x)= C ( x - α ) ( x - β ) where C is a constant.
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The degree of the remainder is always less than the degree of the divisor in case of polynomial division. ... But degree of (y+5) is 1. So it can't be the remainder.
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A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of x. We can give a general defintion of a polynomial, and define its degree.
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A polynomial equation with two terms usually joined by a plus or minus sign is called a binomial. Binomials are used in algebra. Polynomials with one term will be called a monomial and could look like 7x. A polynomial with two terms is called a binomial; it could look like 3x + 9.
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['Example: Add the polynomials 5x – 2 + y and –3y + 5x + 2.', 'Solution: 5x – 2 + y + (–3y + 5x + 2) ... ', 'Example: Find the sum of –7x3y + 4x2y2 – 2 and 4x3y + 1 – 8x2y2', 'Solution: –7x3y + 4x2y2– 2 + 4x3y + 1 – 8x2y2 ... ', 'Example: Simplify –4x + 7 – (5x – 3) ... ', 'Example: ... ', 'Solution:']
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['multiply each term in one polynomial by each term in the other polynomial.', 'add those answers together, and simplify if needed.']
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If √5 is rational, then it can be expressed by some number a/b (in lowest terms). ... Every composite has a unique prime factorization and can't have both an even and odd number of prime factors. This contradiction forces the supposition wrong, so √5 cannot be rational. It is, therefore, irrational.
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logx is just a numeric quantity. As it is ten raised to a real no. Hence,it is not a polynomial.
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We have been given α and β are the zeroes of the polynomial such that α + β= 6 and αβ = 4 . Therefore, Required Polynomial will be x² - 6x + 4.
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All the exponents in the algebraic expression must be non-negative integers in order for the algebraic expression to be a polynomial. As a general rule of thumb if an algebraic expression has a radical in it then it isn't a polynomial.
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It is same as (x^2 - 4x -5). So in any case, x is less than 5.
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Square root of 5. It is an irrational algebraic number.
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The difference between a polynomial and a polynomial function is mainly a difference of viewpoint. ... Remember that two polynomials a(x) and b(x) are equal iff corresponding coefficients are equal, whereas two functions a(x) and b(x) are equal a(x)=b(x) for every x in their domain.
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Polynomial functions are nothing more than a sum of power functions. As a result, certain properties of polynomials are very "power-like." When many different power functions are added together, however, polynomials begin to take on unique behaviors.