Question

Choose the correct classification of 5x + 2x2 − 8 by number of terms and by degree.

Third degree polynomial

Fourth degree trinomial

Second degree trinomial

Sixth degree polynomial

Choose the polynomial that is written in standard form.

xy3 + 4x5y + 10x3

x4y2 + 4x2y + 8x

−9x4y2 + 4x3y5 + 10x2

x6y3 + 4x4y8 + x2

Answer 1

The degree of a polynomial is always the highest power of one of its variables. In this case, x^2 is the highest power, which would make it...? ;)
A term is basically each product that are usually added or subtracted - here you've got three different products (5*x, 2*x^2, and 1*8), so three terms (that's got nothing to do with the degree of the polynomial though).

Answer 2

The standard form means only that the terms are ordered by their degrees - basically, the term with the highest exponent comes first, then the term with the second highest exponent, and so on.
For example,

\[2x ^{3} + 4x ^{2} - 3x\]

Would be standard form.

Answer 3

so it would be the second degree trinomial?

Answer 4

Correct.