Question

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

Explanation:

Step1: Analyze the definition of a binomial

A binomial is a polynomial with two terms. So we first check the number of terms in each option:

• Option A: \(8x^{3}+2x + 3\) has three terms (trinomial), so eliminate A.
• Option B: \(x^{3}-x^{2}+8\) has three terms (trinomial), so eliminate B.
• Option C: \(2x^{8}+3\) has two terms (binomial), but the degree is 8 (since the highest power of \(x\) is 8), not 3, so eliminate C.
• Option D: \(- 5x^{3}+8\) has two terms (binomial), the highest power of \(x\) is 3 (so degree 3), and the constant term is 8 (the term without \(x\)).

Answer:

D. \(-5x^{3}+8\)