Question

Classify each polynomial by its degree and by its number of terms.

Answer 1

Answer:

a. Degree 4; 2 terms

b. Degree 2; 3 terms

c. Degree 3; 1 term

Step-by-step explanation:

Here, all you need is a few definitions. The "degree" of a polynomial is just the highest exponent you see, and be careful with this, because sometimes the exponents won't be arranged from high to low. In this case, they are. In a polynomial, a "term" is basically anything that sits between a plus/minus operation (i.e in 5x + 4, 5x and 4 are both "terms").

a. What's the highest exponent you see? 4. So the degree is 4. You have 5x^4 and 8 separated by a minus sign, so that'll be 2 terms.

b. The highest exponent here is just 2, so it's a degree 2 polynomial. Two minus signs, so count 'em up: 3 terms.

c. Highest exponent is 3, and since 9m^3 sits on its own, you only have the one term.

Note that something like 3abc is one term. 3a/b is also one term. So is 4ab^2cd. If it's being multiplied or divided, they're together like a family. Addition or subtraction separates terms; multiplication and division don't.