Question

What is the degree of `16x^4yz + 12x^2y^3z - 24x^3y^2z - 18xy^4z`?

Answer 1

`6`

Explanation:

Defining Degree
Recall that the degree of a polynomial is the largest sum of the exponents of each of the variables in a term within the polynomial.

Finding the Degree
`1`. Start by locating the terms of the polynomial.

`underbrace(16x^4yz)_color(blue)("term")+underbrace(12x^2y^3z)_color(blue)("term")-underbrace(24x^3y^2z)_color(blue)("term")-underbrace(18xy^4z)_color(blue)("term")`

`2`. Determine the degree of each term by adding the exponents of each variable within the term. Recall that the exponent on a term like `x` or `y` is `1`.

`a)` `16x^color(red)4y^color(purple)1z^color(gray)1color(brown)(rArr)color(red)4+color(purple)1+color(gray)1stackrel(color(teal)("degree "))(color(brown)(rArr))6`

`b)` `12x^color(red)2y^color(purple)3z^color(gray)1color(brown)(rArr)color(red)2+color(purple)3+color(gray)1stackrel(color(teal)("degree "))(color(brown)(rArr))6`

`c)` `24x^color(red)3y^color(purple)2z^color(gray)1color(brown)(rArr)color(red)3+color(purple)2+color(gray)1stackrel(color(teal)("degree "))(color(brown)(rArr))6`

`d)` `18x^color(red)1y^color(purple)4z^color(gray)1color(brown)(rArr)color(red)1+color(purple)4+color(gray)1stackrel(color(teal)("degree "))(color(brown)(rArr))6`

`3`. Since the degree for each term is `6`, the degree of the whole polynomial is also `6`. This can be written mathematically as:

`color(green)(|bar(ul(color(white)(a/a)"deg"(16x^4yz+12x^2y^3z-24x^3y^2z-18xy^4z)=6color(white)(a/a)|)`