Question

justify reasoning determine whether each of the following statements is true or false. justify your argument.
a. a binomial can have a degree of zero │ true │ a binomial must have │ select choice │ monomial
term with degree greater than zero
b. the order in which polynomials are subtracted does not matter │ false │ ( (2x - 3) - (4x - 3) = )
│ select choice │ but ( (4x - 3) - (2x - 3) = ) │ select choice │

Explanation:

Step1: Analyze part a (first statement)

A binomial has 2 terms. A degree 0 binomial would be like $5 + 3$, both terms degree 0. But a binomial does not require terms with degree >0. So the first statement is False.

Step2: Analyze part a (second statement)

A binomial needs two distinct terms, but they can be degree 0. So "A binomial must have a term with degree greater than zero" is False.

Step3: Simplify part b first expression

Distribute the subtraction:
$(2x - 3) - (4x - 3) = 2x - 3 - 4x + 3$
Combine like terms: $2x - 4x + (-3 + 3) = -2x$

Step4: Simplify part b second expression

Distribute the subtraction:
$(4x - 3) - (2x - 3) = 4x - 3 - 2x + 3$
Combine like terms: $4x - 2x + (-3 + 3) = 2x$
Since $-2x
eq 2x$, subtraction order matters, so the statement is False.

Answer:

a. First statement: False
Second statement: False
b. $(2x - 3) - (4x - 3) = -2x$
$(4x - 3) - (2x - 3) = 2x$
Statement: False