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# What is the degree of the polynomial (x^4+ax^7+bx+c)(x^3+dx^2+e)(x+f), where letters a through f are all nonzero constants?

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What is the degree of the polynomial (x^4+ax^7+bx+c)(x^3+dx^2+e)(x+f), where letters a through f are all nonzero constants?

Thanks a bunch!

Nov 29, 2017

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The degree of the polynomial  is found by the product of the first terms in each set of parentheses....thus......we have

x^4 * x^3 * x   =   x^8   ⇒    degree 8

Nov 29, 2017
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It is generally considered standard to write polynomials from highest degree to least degree, so your method of multiplying the first term in every polynomial would be sufficient. However, the first polynomial actually has a degree of 7

(\(x^4+\textcolor{red}{ax^7}+bx+c\)). Notice that the highest-degree term is actually listed second.

Therefore, I would amend your rule slightly. Add the degree of each polynomial together during multiplication. Doing this will give you the degree of \((x^4+\textcolor{red}{ax^7}+bx+c)(\textcolor{red}{x^3}+dx^2+e)(\textcolor{red}{x}+f)\) or any other product of multiple polynomials. Notice that I have highlighted, in red, the term that dictates the degree of the individual polynomials. If we use the rule that I aforementioned, then the degree equals \(7+3+1=11\).

TheXSquaredFactor  Nov 29, 2017