monomial help?

Question

I am doing homework and I can't figure these last three problems out:

4r^4w^2 + 9r^2w^6 -r^6w^2

(would that one be: 3r^6w^2 + 9rw^6)?

t^-5(t^2 - t^4 + 5t)


and, the worst one:

[x^(7y+1)]/ [ x^(7y-5)]

any help would be appreciated

Answer 1

4r^4 w^2 + 9r^2 w^6 - r^6 w^2

First, combine terms if possible. We can't do any combining of terms here; that would require that two or more terms had the same power of r and the same power of w.

Next, determine the largest common constant factor for the three terms, and the smallest power of each variable, then factor that out.

The largest common constant is 1
The smallest power of r is r^2
The smallest power of w is w^2

So factor out r^2 w^2:

4r^4 w^2 + 9r^2 w^6 - r^6 w^2 = r^2 w^2(4r^2 + 9 w^4 - r^4)

The terms in the parentheses don't factor, so we're done.

t^-5(t^2 - t^4 + 5t)

I'm not sure what your teacher would consider the simplified form. We can factor t^1 out of the terms in the parentheses, which we can combine with the t^-5:

t^-5(t^2 - t^4 + 5t) = t^(-5) t (t - t^3 + 5) = t^(-4) (t - t^3 + 5)

Should we get rid of the negative power by writing this as a fraction? If so,

t^(-4) (t - t^3 + 5) = (t - t^3 + 5) / (t^4)

The last one is actually the easiest. Recall that

(x^a) / (x^b) = x^(a-b) even if a and b are complicated expressions. So

[x^(7y+1)]/ [ x^(7y-5)] = x^[(7y+1) - (7y-5)] = x^6

Answer 2

Monomial, binomial or trinomial refers to the numbers of terms in the expresion (NOT the degree of the polymomial). The signs + and - separate in terms, so the first one has 3 terms, therefore is trinomial, the second one is monomial and the third one is binomial 34x + x^2 + z T wxy^3z^2 M pn^2 - 13n^3 B