Question

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Answer 1

Expression (5x² - 2x + 7), ($\frac{1}{5}x^3 -\frac{7}{2}x^2 -2$) and (y⁵ - √(5y²) + 7) are polynomials.

What is a polynomial ?

A polynomial is a type of algebraic expression where exponents of all variables are whole number.

1) 5x² - 2x + 7

Since there are no variables raised to negative or fraction exponents,

the expression is a polynomial.

2) $\frac{1}{5}x^3 -\frac{7}{2}x^2 -2$

Since there are no variables raised to negative or fraction exponents,

the expression is a polynomial.

3) y⁵ - √(5y²) + 7

This can be re-written as

$y^5-(\sqrt{5})y+7$

Since there are no variables raised to negative or fraction exponents,

the expression is a polynomial.

4) $\frac{y^3}{3} -\sqrt{y} +2$

This can be re-written as

$\frac{1}{3}y^2 -y^{1/2}+2$

Since variable y is raised to a fraction exponent,

the expression is not polynomial.

Therefore, expression (5x² - 2x + 7), ($\frac{1}{5}x^3 -\frac{7}{2}x^2 -2$) and (y⁵ - √(5y²) + 7) are polynomials.

Learn more about polynomials here: brainly.com/question/17822016

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