Question

For the polynomial 6xy2-5x?y?+9x? to be a trinomial with a degree of 3 after it has been fully simplified, what is the

missing exponent of the y in the second term?
0
e 1
2.
x 3

Answer 1

The exponent of y is 1

Explanation:

Given

`6xy^2 - 5x^([])y^([]) + 9x^([])`

`degree = 3`

Required

The exponent of y (second term)

Since the polynomial has a degree of 3, the exponents of y will decrease from left to right (i.e. 2,1,0) while x will increase from left to right (i.e. 1,2,3)

So, we have:

`6xy^2 - 5x^([])y^([]) + 9x^([]) = 6xy^2 - 5x^([2])y^([1]) + 9x^([3])`

Remove square brackets

`6xy^2 - 5x^([])y^([]) + 9x^([]) = 6xy^2 - 5x^2y + 9x^3`

The second term is:

`T_2 =5x^2y`

The exponent of y is 1