Question

PLEASE HELP ME! Drag the expressions into the boxes to correctly complete the table.

Answer 1

The polynomials are:

$x^4+3x^3-5x^2-7x+20$

$x^3-2x^2+x-12$

$x^2+3x^5-6x+12x^3$

Not a polynomial are:

$4\sqrt[3]{x} -\sqrt{x} -20$

$\frac{5}{x^3}-\frac{1}{x^2}+\frac{8}{x}-40$

$x^{-3}-x^{-2}-6x^{-1}+8$

Solution:

Polynomial is an expression with variables and coefficients,

Which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables

Option 1

$4\sqrt[3]{x} -\sqrt{x} -20$

Polynomial does not include roots

This is not a polynomial equation

Option 2

$x^4+3x^3-5x^2-7x+20$

This is polynomial expression involving addition and subtraction between terms with non-negative integer exponents of variables

Option 3

$\frac{5}{x^3}-\frac{1}{x^2}+\frac{8}{x}-40$

This is not a polynomial. This equations involves negative integer exponents of variables

Option 4

$x^3-2x^2+x-12$

This is a polynomial involving addition and subtraction between terms with non-negative integer exponents of variables

Option 5

$x^{-3}-x^{-2}-6x^{-1}+8$

This is not a polynomial. This equations involves negative integer exponents of variables

Option 6

$x^2+3x^5-6x+12x^3$

This is a polynomial involving addition and subtraction between terms with non-negative integer exponents of variables