Questions: Add. 6 x^3 - 2 x^2 + 5 x - 2 and -3 x^3 + 4 x^2 - 1 The sum is □ (Simplify your answer.)

Solution Steps

To add the given polynomials, combine like terms. This involves adding the coefficients of terms with the same degree.

We have two polynomials to add: \[ P_1 = 6x^{3} - 2x^{2} + 5x - 2 \] \[ P_2 = -3x^{3} + 4x^{2} - 1 \]

To find the sum \( P_1 + P_2 \), we combine the coefficients of like terms:

• For \( x^{3} \): \( 6 - 3 = 3 \)
• For \( x^{2} \): \( -2 + 4 = 2 \)
• For \( x \): \( 5 + 0 = 5 \)
• For the constant term: \( -2 - 1 = -3 \)

Thus, the combined polynomial is: \[ P_{\text{sum}} = 3x^{3} + 2x^{2} + 5x - 3 \]

Final Answer