Question

ALGEBRA 1

Which expressions are polynomials?
A. 35x^2
B. 4x+x√−1
C. 7x^7−x^−5
D. x/5+2

Answer 1

The main thing about a polynomial is it's the sum of terms, each a constant coefficient times whole number power (0, 1, 2, 3, ...) of the variable.

A. 35x² is a polynomial; the power 2 is a whole number. There's only one term so not really the sum of terms, but one's enough.

B.
`4x + x √(-1) = (4+i)x`

That's a perfectly good polynomial but you might not have gotten to it in algebra I yet. The square root of negative 1 is abbreviated i and when we add it to the set of real numbers we get complex numbers. It has a complex coefficient 4+i but that's OK in a polynomial.

If you haven't gotten to complex numbers yet you might be expected to answer no to this one. I don't know.

C.
`7x^7 - x^(-5)`

The negative exponent means this isn't a polynomial.

D. x/5 + 2

That's fine, just another way of writing

`\frac 1 5 x + 2`

which is a perfectly ok polynomial.

Answer: A B D