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College Algebra
Chapter 1/Section 4
Tell whether the expression is a polynomial. If it is, give the degree. If it's not a monomial, state the reason.
18. 1 - 4x...This is a polynomial. The degree is 1.
20. -pi...This is a polynomial. I say -pi = -pi(x^0). Since x^0 = 1, then the degree is 0.
22. (3/x) + 2...This is not a polynomial because (3/x) is actually 3x^(-1). The negative degree removes the polynomial definition.
24. 10z^2 + z...This is a polynomial. The degree is 2.
26. (3x^3 + 2x - 1)/(x^2 + x + 1)
Although the top and bottom expressions are polynomials individually, the bottom polynomial has a degree greater than 0. So, this algebraic fraction is not a polynomial.
Note: For 26, why can't a polynomial in an algebraic fraction that has a degree greater than 0 in the denominator not be a polynomial as a fraction?
Chapter 1/Section 4
Tell whether the expression is a polynomial. If it is, give the degree. If it's not a monomial, state the reason.
18. 1 - 4x...This is a polynomial. The degree is 1.
20. -pi...This is a polynomial. I say -pi = -pi(x^0). Since x^0 = 1, then the degree is 0.
22. (3/x) + 2...This is not a polynomial because (3/x) is actually 3x^(-1). The negative degree removes the polynomial definition.
24. 10z^2 + z...This is a polynomial. The degree is 2.
26. (3x^3 + 2x - 1)/(x^2 + x + 1)
Although the top and bottom expressions are polynomials individually, the bottom polynomial has a degree greater than 0. So, this algebraic fraction is not a polynomial.
Note: For 26, why can't a polynomial in an algebraic fraction that has a degree greater than 0 in the denominator not be a polynomial as a fraction?