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 less than one 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
select choice
-2x
6x - 6
2x - 6
2x

Explanation:

Step1: Evaluate part a logic

A binomial is defined as a polynomial with two distinct monomial terms. For a binomial to have a degree of 0, both terms would need to be constant terms (degree 0), but combining like constant terms results in a single monomial, not a binomial. A binomial requires at least one term with degree > 0 to have two unique non-combinable terms.

Step2: Calculate first subtraction (part b)

Simplify $(2x - 3) - (4x - 3)$ by distributing the negative sign and combining like terms:
$2x - 3 - 4x + 3 = (2x - 4x) + (-3 + 3) = -2x$

Step3: Calculate second subtraction (part b)

Simplify $(4x - 3) - (2x - 3)$ by distributing the negative sign and combining like terms:
$4x - 3 - 2x + 3 = (4x - 2x) + (-3 + 3) = 2x$

Answer:

a. False; A binomial must have at least one monomial term with degree greater than zero.
b. $(2x - 3) - (4x - 3) = -2x$ but $(4x - 3) - (2x - 3) = 2x$