For the polynomial 6xy2 – 5x2y? + 9x2 to be a trinomial with a degree of 3 after it has been fully simplified, the missing exponent of the y-term must be ?

The missing exponent of the y-term must be 1.

is a trinomial with a degree of 3 after it has been fully simplified

Step-by-step explanation:

 Given :  The polynomial be a trinomial with a degree of 3  after it has been fully simplified.

We have to find the value of the missing exponent of the y-term that is a.

Consider the Given polynomial

Since after simplification a trinomial is obtained so the  missing exponent of the y-term in the polynomial  

Since the degree of polynomial is 3.

So the highest power of the polynomial has to be 3 and rest terms have power less than 3.

In , , has highest power 3 (1+2) so the combined power of has to be three or less than 3.

And power of y must lies in between 0 ≤ a ≤ 1

If power of y is 0 then  becomes becomes an simplified to   which is not trinomial.

Hence  a has to be 1.

So that   becomes   which is a trinomial with a degree of 3 .

Thus, the missing exponent of the y-term must be 1.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80