Questions: Perform this subtraction: (9 x^5 - x^2 + 4 x) - (-3 x^5 + x^2 - 1)

Solution Steps

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

To subtract the polynomial \(-3x^5 + x^2 - 1\) from \(9x^5 - x^2 + 4x\), first distribute the negative sign across the second polynomial: \[ -( -3x^5 + x^2 - 1 ) = 3x^5 - x^2 + 1 \]

Add the resulting polynomial from Step 1 to the first polynomial: \[ (9x^5 - x^2 + 4x) + (3x^5 - x^2 + 1) \]

Combine the like terms:

• For \(x^5\) terms: \(9x^5 + 3x^5 = 12x^5\)
• For \(x^2\) terms: \(-x^2 - x^2 = -2x^2\)
• For \(x\) terms: \(4x\) (no like term to combine)
• Constant term: \(1\)

The resulting polynomial after combining like terms is: \[ 12x^5 - 2x^2 + 4x + 1 \]

Final Answer