Question

Julian fully simplifies this polynomial and then writes it in standard form.

4x2y2 – 2y4 – 8xy3 + 9x3y + 6y4 – 2xy3 – 3x4 + x2y2
If Julian wrote the last term as –3x4, which must be the first term of his polynomial in standard form?

A. 4y4
B, 6y4
C. –2xy3
D. –10xy3

Answer 1

Combine like terms:
- y^4: -2y^4 + 6y^4 = 4y^4
- x^2y^2: 4x^2y^2 + x^2y^2 = 5x^2y^2
- xy^3: -8xy^3 - 2xy^3 = -10xy^3

So the simplified polynomial is
-3x^4 + 9x^3y + 5x^2y^2 - 10xy^3 + 4y^4.

If Julian wrote -3x^4 as the last term, he is putting terms in increasing powers of x, so the first term must be 4y^4.

Answer: A. 4y^4