Polynominals ???

Question

I need to find the missing polynominal. Can someone explain how to do that. I know the answer is 7n... but how to get it?

(3x^2+2xy-1)+(x^2+xy+5)+(?)=5x^2-3xy+3

Answer 1

(3x^2 + 2x - 1) + (x^2 + xy + 5) + (?) = 5x^2 - 3xy + 3

All you have to do is assign z to the unknown (question mark), and solve for z.

(3x^2 + 2x - 1) + (x^2 + xy + 5) + z = 5x^2 - 3xy + 3

Let's start off by grouping like terms on the left hand side.

4x^2 + 2x + xy + 4 + z = 5x^2 - 3xy + 3

Now, let's move everything but the z to the right hand side.

z = 5x^2 - 3xy + 3 - 4x^2 - 2x - xy

Group like terms,

z = x^2 - 3xy - 2x - xy

And we've just solved for z.

Answer 2

Add the 2 things in parantheses (3x^2... and x^2...)

then subtract this from the polynomial on the right side of the equation. This is the answer.

Answer 3

3x^2+2xy-1+x^2+xy+5
-5x^2-3xy+3=-p(x)
p(x)=x^2-7