Question

Question 1 Which of the following expressions are polynomials? Justify your answer. I. 8 II. √3x2−2x III. 1−√5x IV. 15x−2+5x+7 V. (x−2)(x−4)x VI. 1x+1 VII. 17a3−2√3a2+4a−7 VIII. 12x

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Solution

i. Polynomial. Because, the exponent of the variable of 8 or 8x0 is 0 which is a whole number. ii. Polynomial. Because, the exponent of the variable of √3x2−2 is a whole number. iii. Not a polynomial. Because, the exponent of the variable of 1−√5x or 1−√5x12 is 12 which is not a whole number. iv. Polynomial. Because, the exponents of the variable of 15x−2+5x+7=15x2+5x+7 are whole numbers. v. Not a polynomial. Because, the exponent of the variable of (x−2)(x−4)x=x2−6x+8x=x−6+8x−1 is -1, which is not a whole number. vi. Not a polynomial as the polynomial is expressed as a0+a1x+a2xn, where a0,a1,a2⋯,an are constants. Now, the given function is in the form f(x)=p(x)q(x) is a rational expression but not a polynomial. vii. Polynomial. Because, the exponents of the variable of 17a3−2√3a2+4a−7 are whole numbers. viii. Not a polynomial. Because, the exponent of the variable of 12x or 12x−1 is -1, which is not a whole number.

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