Question

When calculating the degree of a polynomial for the purpose of graphing, do you add all exponents together to find odd or even?

Answer 1

No. We are concerned with only the highest exponent.

Answer 2

the degree is the highest power in the equation

Answer 3

so, for example... x^19 +y^10 +z^3 would count as "odd?"

Answer 4

since 19 is an odd number.

Answer 5

Yes.

Answer 6

\(x^3 + x^2 \) is odd; \(x^2+x\) is even;

Answer 7

f(x) = a(x – b)^2(x – c)^3

that would be degree 5, though, right?

Answer 8

yes

Answer 9

wouldn't that be x^2+1=x^3?

Answer 10

\[a(x^2-2bx+b^2)(x^3+3xc^2-3x^2c-c^3)\]

Answer 11

\[=a(x^5+3x^3c^2-3x^4c-c^3x^2-2bx^4-3x^2bc+3x^3bc+2bxc^3+\]\[...x^3b^2+3xb^2c^2-3x^2b^2c-b^2c^3\]
\[=x^5a+3x^3ac^2-3x^4ac-ac^3x^2-2x^4ab-3x^2abc+3x^3abc+2xabc^3+...x^3ab^2+3xab^2c^2-3x^2ab^2c-ab^2c^3\]

Answer 12

you can simplify it but you get the picture

Answer 13

So it's just easier to add the exponents together, when multiplying two factors? At least to determine whether the multiplicity is odd or even?

Answer 14

Yes, definitely. But make sure both exponents are raising the same base.