We need to complete each one of the given sentences.
The solutions are:
1) b
2) c
3) c
4) d
1) A monomial is a polynomial of a single term.
If we multiply two monomials, for example:
p(x) = a*x^n
q(x) = b*x^m
We get:
p(x)*q(x) = (a*x^n)*(b*x^m) = (a*b)*x^(n + m)
So we can see that this is a monomial, then the correct option here is b: always.
2) If we have one term multiplicating two terms (binomial means two terms) we can never have 3 terms (trinomial). Then the correct option is c, never.
3) two binomials can be written as
p(x) = a*x^n + b*x^m
q(x) = c*x^k + d*x^z
The product will have 4 terms, because these are binomials, we must have that:
n ≠ m
k ≠ z
Then the exponents of the resulting terms will be different (we will have at least two different exponents) this means that we can't have a monomial, then the correct option is c, never.
4) A binomial has 2 terms, a trinomial 3 terms, then the product between these has:
2*3 = 6 terms.
The correct option is d.
If you want to learn more, you can read:
https://brainly.com/question/8985142
