Question

How do you identify the coefficients, variable terms (with exponents), and constants in the following expression `4z^5-8x^2-6`?

Answer 1

`color(green)(4)color(red)(z)^(color(blue)(5)) - color(green)(8)color(red)(x)^(color(blue)(2)) - color(orange)(6)`

`color(green)("Coefficients")`
`color(red)("Variables")`
`color(blue)("Exponents")`
`color(orange)("Constants")`

Explanation:

The expression is `4z^5 - 8x^2 - 6`.

The variable terms, shown in red, are x and z.

`4color(red)(z)^5 - 8color(red)(x)^2 - 6`

This is because these terms can be assigned different values which will change the value of the expression.

The exponents of the variable terms, shown in blue, are the powers to which these variables are raised to.

`4color(red)(z)^(color(blue)(5)) - 8color(red)(x)^(color(blue)(2)) - 6`

The coefficients of the variable terms, shown in green, are the constant values in front of the variable terms:

`color(green)(4)color(red)(z)^(color(blue)(5)) - color(green)(8)color(red)(x)^(color(blue)(2)) - 6`

Finally, the constants of the equation, shown in orange are the terms which will not change no matter what values are assigned to the variables.

`color(green)(4)color(red)(z)^(color(blue)(5)) - color(green)(8)color(red)(x)^(color(blue)(2)) - color(orange)(6)`