Given two polynomial expressions, ( P(x) = 3x^3 - 2x^2 + 4x - 1 ) and ( Q(x) = 2x^3 + 3x^2 - 5x + 2 ). Compute the sum of ( P(x) ) and ( Q(x) ).

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Step:1 ：First, we align the polynomials vertically by their like terms: [begin{align*} &3x^3 - 2x^2 + 4x - 1 &+2x^3 + 3x^2 - 5x + 2end{align*}]Step:2 ：Then, we add the like terms together: [begin{align*} &(3x^3 + 2x^3) + (-2x^2 + 3x^2) + (4x - 5x) + (-1 + 2) &=(5x^3) + (x^2) + (-x) + (1)end{align*}]Step:3 ：Finally, we write the sum as a single polynomial: ( 5x^3 + x^2 - x + 1 )

Answer

Step: 1 ：First, we align the polynomials vertically by their like terms: [begin{align*} &3x^3 - 2x^2 + 4x - 1 &+2x^3 + 3x^2 - 5x + 2end{align*}]Step: 2 ：Then, we add the like terms together: [begin{align*} &(3x^3 + 2x^3) + (-2x^2 + 3x^2) + (4x - 5x) + (-1 + 2) &=(5x^3) + (x^2) + (-x) + (1)end{align*}]Step: 3 ：Finally, we write the sum as a single polynomial: ( 5x^3 + x^2 - x + 1 )

Given two polynomial expressions, \( P(x) = 3x^3 - 2x^2 + 4x - 1 \) and \( Q(x) = 2x^3 + 3x^2 - 5x + 2 \). Compute the sum of \( P(x) \) and \( Q(x) \).

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