Question

which could be the missing first term of the expression that, when fully simplified, would be a binomial with a degree of
8? select three options.
\underline{qquad}- 5xy^3 + 9x^2y
\bigcirc 0
\bigcirc 5xy^3
\bigcirc 9x^2y
\bigcirc 8y^8
\bigcirc 4xy^3

Explanation:

Step1: Recall binomial & degree rules

A binomial has 2 terms; degree = highest sum of variable exponents in a term. For a term $ax^my^n$, degree is $m+n$.

Step2: Test Option 0

Add 0 to the expression: $0 -5xy^3 +8x^2y = -5xy^3 +8x^2y$. This is a binomial. Degree of $-5xy^3$ is $1+3=4$, degree of $8x^2y$ is $2+1=3$. Highest degree is 4.

Step3: Test Option $5xy^3$

Add to expression: $5xy^3 -5xy^3 +8x^2y = 8x^2y$. This is a monomial (1 term), invalid.

Step4: Test Option $8x^2y$

Add to expression: $8x^2y -5xy^3 +8x^2y = -5xy^3 +16x^2y$. This is a binomial. Degree of $-5xy^3$ is 4, degree of $16x^2y$ is 3. Highest degree is 4.

Step5: Test Option $3y^4$

Add to expression: $3y^4 -5xy^3 +8x^2y$. This is a trinomial (3 terms), invalid.

Step6: Test Option $-4xy^3$

Add to expression: $-4xy^3 -5xy^3 +8x^2y = -9xy^3 +8x^2y$. This is a binomial. Degree of $-9xy^3$ is 4, degree of $8x^2y$ is 3. Highest degree is 4.

Answer:

0, $8x^2y$, $-4xy^3$