Identify the degree of the polynomial 8x^3y^2 – 10xy + 4x^2y^2 + 3.

2 answers:

3 0

When the polynomial has more than one variable you have to sum the exponents of the variables for every monomial. The largest sum is the order of the polynomial.

Here:

momomial sum of the exponents
8x^3y^2 3 + 2 = 5
-10xy 1 + 1 = 2
4x^2y^2 2 + 2 = 4

Then the degree is 5.

pishuonlain [190]3 years ago

3 0

Answer:

The degree of the polynomial is 5

Step-by-step explanation:

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Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.

marishachu [46]

Answer:

$\text{Possible rational zeros}=\pm1,\pm\frac{1}{2},\pm2,\pm3,\pm\frac{3}{2},\pm6,\pm9,\pm\frac{9}{2},\pm18$

Step-by-step explanation:

We have been given the function

$f(x)=-2x^2+4x^3+3x^2+18$

From the rational zeros theorem, we have

$\text{Possible rational zeros}=\pm\frac{\text{Factors of constant term}}{\text{Factors of leading coefficient}}$

From the given function,

Leading coefficient = 2

Factors of 2 are 1,2

Constant term = 18

Factors of constant term = 1, 2, 3, 6, 9, 18

Hence, we have

$\text{Possible rational zeros}=\pm\frac{1,2,3,6,9,18}{1,2}\\\\\text{Possible rational zeros}=\pm1,\pm\frac{1}{2},\pm2,\pm3,\pm\frac{3}{2},\pm6,\pm9,\pm\frac{9}{2},\pm18$