Question

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 1

1. 5
2. 6
 The sum will be degree: 5
The maximum number of terms of the sum is: 6

Answer 2

The sum of polynomials of given condition will have 5 degree and maximum of 6 terms.

Given information:

Raj writes a polynomial of one variable with degree 5 and four terms.

Nicole writes a polynomial of one variable with degree 2 and 3 terms.

Let the variable be a.

The polynomial made by Raj could be,

${a}^{5} + {a}^{4} + {a}^{3} + 1$

the above polynomial is a 5 degree one variable polynomial with four terms.

The polynomial made by Nicole could be,

${a}^{2} - 3a + 4$

the above polynomial is a 2 degree one variable polynomial with three terms.

Now, the addition of two polynomials will be,

${a}^{5} + {a}^{4} + {a}^{3} + {a}^{2} - 3a + 5$

The above polynomial has degree 5 and maximum number of terms 6.

Therefore, the sum of polynomials of given condition will have 5 degree and maximum of 6 terms.

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