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Which One Doesn't Belong: What are Polynomials? Which one doesn't belong?

A. 4-x^2+x^3-4x
B. 2x^4+x^2-5.7x+2
C. x^2+7x-x 1/3 +2
D. x^5+8.36x^3-2.

User Eugenekgn
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Final answer:

In the context of which expression doesn't belong when comparing polynomials, option C: x^2+7x-x 1/3 +2 does not belong because it contains an exponent that is not a whole number, making it a non-polynomial. Options A, B, and D are polynomials. For linear equations, options A and B are linear while C is not provided.

Step-by-step explanation:

Polynomials are algebraic expressions that consist of variables and coefficients, with the variables raised to whole-number exponents and combined with addition, subtraction, and multiplication (but not division by a variable). For example, 2x^4+x^2-5.7x+2 is a polynomial.

Looking at the options provided in the question, they all appear to be expressions that may possibly be polynomials. However, upon closer examination, option C: x^2+7x-x 1/3 +2 includes a term with an exponent of 1/3, which makes it a non-polynomial. Thus, option C does not belong as it contains a term with a fractional exponent, which is not allowed in polynomials.

In the reference to Practice Test 4 about linear equations, linear equations are those where the variables are raised only to the first power and appear in no other form. The equations A: y=-3x and B: y=0.2+0.74x are both examples of linear equations, as they depict a relationship where y varies directly with x, with no other exponents on x except 1.

User Marko Hlebar
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