Question

Raj and Nicole's polynomial expressions are added to create a sum, written in standard form. What can you determine about the degree of the sum? The sum will be degree . What can you determine about the number of terms of the sum? The maximum number of terms of the sum is , but it could be less.

Answer 1

Complete question is;

raj writes a polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5. Nicole writes a polynomial expression in standard form using one variable, a, that has 3 terms and is degree 2. Raj and Nicole’s polynomial expressions are added to create a sum, written in standard form. What can you determine about the degree of the sum? The sum will be degree . What can you determine about the number of terms of the sum? The maximum number of terms of the sum is , but it could be less.

Answer:

Degree: 5

Maximum number of terms: 6 or could less

Step-by-step explanation:

We are told that Raj writes a polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5. So let this polynomial be: Aa^(5) + Ba³ + Ca + D

Also, we're told that: Nicole writes a polynomial expression in standard form using one variable, a, that has 3 terms and is degree 2.

The polynomial is: Ea² + Fa + G

If we add both polynomials we, we will get;

Aa^(5) + Ba³ + Ca + D + Ea² + Fa + G

Rearranging terms to give;

Aa^(5) + Ba³ + Ea² + Ca + Fa + D + G

Collecting like terms to give;

Aa^(5) + Ba³ + Ea² + a(C + F) + (D + G)

So this is now a 5 degree polynomial.

So the new sum will have a degree of 5.

Also, as seen in the above steps, the maximum number of terms could be 6 or less.