Question

pick the expression that matches this description:
a $3^{\text{rd}}$ degree binomial with a constant term of 8
choose 1 answer:
\\(\boldsymbol{\text{a}}\\) \\(2x^8 + 3\\)
\\(\boldsymbol{\text{b}}\\) \\(8x^3 + 2x + 3\\)
\\(\boldsymbol{\text{c}}\\) \\(x^3 - x^2 + 8\\)
\\(\boldsymbol{\text{d}}\\) \\(-5x^3 + 8\\)

Explanation:

Step1: Define 3rd degree binomial

A 3rd degree binomial has 2 terms, with the highest exponent of $x$ being 3, plus a constant term.

Step2: Check constant term =8

Eliminate options where the constant term is not 8: Option A (constant=3), Option B (constant=3) are rejected.

Step3: Verify binomial (2 terms)

Option C has 3 terms ($x^3, -x^2, 8$), so it is a trinomial, not a binomial. Reject Option C.

Step4: Confirm valid expression

Option D: $-5x^3+8$ has 2 terms, highest degree 3, constant term 8.

Answer:

D. $-5x^3 + 8$