Which terms could be used as the first term of the expression below to create a polynomial written in standard form? check all that apply. + 8r2s4 – 3r3s3 s5 3r4s5 –r4s6 –6rs5

      The terms that could be used as the first term of the given polynomial  expression to create a polynomial written in standard form are;

Option B; 3r⁴s⁵

Option C; -r⁴s⁶

Option D; -6rs⁵

The options are;

A) s⁵

B) 3r⁴s⁵

C) -r⁴s⁶

D) -6rs⁵

We are given the polynomial expression;

+8r²s⁴ - 3r³s³

     Now, the two terms of the given polynomial will each have a degree of 6. This is because the sum of their exponents is the degree;

For +8r²s⁴, we add the exponents to get 2 + 4 = 6

Also for 3r³s³, we add the exponents to get 3 + 3 = 6

     This means that for any term that will start the polynomial must have a degree greater than 6.

Option A;  s⁵ cannot start the polynomial because it has a degree of 5 which is less than 6.

Option B; 3r⁴s⁵ can start the polynomial because it has a degree of 4 + 5 = 9.

Option C; -r⁴s⁶ can start the polynomial because it has a degree of 4 + 6 = 10.

Option D; The degree of -6rs⁵ is 6 but it can also start the polynomial because the exponent of s is greater than the other two in the given expression.

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