What is the degree of the Polynomial $3 - 4 z^{4} w^{8} u^{6} 7 u^{9} z w^{8}$ $3-4z^4 w^8u^6 7u^9zw^8$ ?

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Answer 1 · 2015-12-17T22:25:54

The greatest sum of exponents of each of the terms, namely:

$4 + 8 + 6 + 9 + 1 + 8 = 36$ $4+8+6+9+1+8=36$

This polynomial has two terms (unless there is a missing $+$ $+$ or $-$ $-$ before the $7 u^{9} z w^{8}$ $7u^9zw^8$ as I suspect).

The first term has no variables and is therefore of degree $0$ $0$ .

The second term has degree $4 + 8 + 6 + 9 + 1 + 8 = 36$ $4+8+6+9+1+8=36$ , which being greater than $0$ $0$ is the degree of the polynomial.

Note that if your polynomial should have been something like:

$3 - 4 z^{4} w^{8} u^{6} + 7 u^{9} z w^{8}$ $3-4z^4w^8u^6+7u^9zw^8$

then the degree would be the maximum of the degrees of the terms:

$0$ $0$

$4 + 8 + 6 = 18$ $4+8+6 = 18$

$9 + 1 + 8 = 18$ $9+1+8 = 18$

so the degree of the polynomial would be $18$ $18$

What is the degree of the Polynomial 3-4z^4 w^8u^6 7u^9zw^83−4z4w8u67u9zw83-4z^4 w^8u^6 7u^9zw^8?