Question

5x²+9y⁴-3z + ? = 9x²-5y⁴+2z+3​

Answer 1

Answer:

Let the unknown polynomial be p(x),

$5 {x}^{2} + 9 {y}^{4} - 3z + p(x) = 9 {x}^{2} - 5 {y}^{4} + 2z + 3 \: \: \: \: \: \: \: \: \: \: \: \\ p(x) = 9 {x}^{2} - 5 {y}^{4} + 2z + 3 - 5 {x}^{2} - 9 {y}^{4} + 3z \: \: \: \: \: \: \: \: \: \:\\ = 9 {x}^{2} - 5 {x}^{2} - 5 {y}^{4} - 9 {y}^{4} + 2z + 3z + 3 \\ = 4 {x}^{2} - 14 {y}^{4} + 5z + 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, the polynomial p(x) is 4x²-14y⁴+5z+3.