Questions: Perform this subtraction: [ (-2 x^5+2 x^2-7 x)-(9 x^5+3 x^2-3) ]

Solution Steps

To perform the subtraction of two polynomials, distribute the negative sign across the second polynomial and then combine like terms. This involves subtracting the coefficients of terms with the same degree.

We start with the two polynomials: \[ \text{poly1} = -2x^{5} + 2x^{2} - 7x \] \[ \text{poly2} = 9x^{5} + 3x^{2} - 3 \]

Next, we distribute the negative sign across the second polynomial: \[ \text{poly1} - \text{poly2} = (-2x^{5} + 2x^{2} - 7x) - (9x^{5} + 3x^{2} - 3) \] This simplifies to: \[ -2x^{5} + 2x^{2} - 7x - 9x^{5} - 3x^{2} + 3 \]

Now, we combine the like terms:

• For \(x^{5}\): \(-2x^{5} - 9x^{5} = -11x^{5}\)
• For \(x^{2}\): \(2x^{2} - 3x^{2} = -x^{2}\)
• For \(x\): \(-7x\) remains as is.
• The constant term: \(3\)

Thus, the result is: \[ -11x^{5} - x^{2} - 7x + 3 \]

Final Answer