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If the algebraic expression can be written in the form of a(x)/b(x) where a(x) and b(x) are polynomial functions of x and b(x) â‰ 0, then the expression is a rational algebraic expression.

Q: How do you determine whether an expression is rational algebraic expression or not?

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Any positive number is always bigger than a negative number - whether they are rational or irrational.

The same as you would a rational number. Its distance from zero will represent the number, whether it is rational or irrational.

A terminating or repeating decimal is always rational. Whether it is positive or negative makes no difference. So the answer is no it is not always rational, such as -1/pi

Yes, it is.

If it has more than two factors.

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It isn't always possible to determine. For example, it is unknown whether the Euler-Mascheroni constant (0.5772156649...) is rational or irrational.Most famous numbers and constants are known to be rational or irrational. If it can be expressed as a fraction a/b where a and b are integers, it's rational.

If it can't be expressed as a fraction then it is an irrational number

Discuss how you can use the zeros of the numerator and the zeros of the denominator of a rational function to determine whether the graph lies below or above the x-axis in a specified interval?

Statement 1 is true but totally unnecessary. As integer is always a rational and you do not need to convert it to a fraction to determine whether or not it is rational. A negative fraction is can be rational or irrational. The fact that it is negative is irrelevant to its rationality. An integer number over a zero denominator is not defined and so cannot be rational or irrational or anything. It just isn't.

To determine whether a polynomial equation has imaginary solutions, you must first identify what type of equation it is. If it is a quadratic equation, you can use the quadratic formula to solve for the solutions. If the equation is a cubic or higher order polynomial, you can use the Rational Root Theorem to determine if there are any imaginary solutions. The Rational Root Theorem states that if a polynomial equation has rational solutions, they must be a factor of the constant term divided by a factor of the leading coefficient. If there are no rational solutions, then the equation has imaginary solutions. To use the Rational Root Theorem, first list out all the possible rational solutions. Then, plug each possible rational solution into the equation and see if it is a solution. If there are any solutions, then the equation has imaginary solutions. If not, then there are no imaginary solutions.

When the rational number is expressed as a ratio in its simplest form, if the only factors of the denominator are 2 and 5, then the number has a terminating representation. Otherwise it has an infinitely recurring sequence.

1.6667

The decimal shows a repeating pattern. Repeating decimals are rational.

Integers are rational numbers, whether they are positive or negative.

"Rational" is an adjective and so there cannot be "a rational" (and certainly not "an rational"). Any answer would depend on whether the question was about a rational number, a rational person, a rational argument or "a rational" combined with some other noun.

true

A negative sign, by itself cannot affect whether or not a number is rational.