Questions: Add. (5x^3-4x^2+2)+(2x^3+6x^2-10)+(-13x^3+9x^2-5)

Transcript text: Add. \[ \left(5 x^{3}-4 x^{2}+2\right)+\left(2 x^{3}+6 x^{2}-10\right)+\left(-13 x^{3}+9 x^{2}-5\right) \]

Solution

Solution Steps

To add the given polynomials, we need to combine like terms. This involves adding the coefficients of the terms with the same degree. Specifically, we will add the coefficients of the \(x^3\), \(x^2\), and constant terms separately.

Step 1: Identify Like Terms

The given expression is the sum of three polynomials: \[ (5x^3 - 4x^2 + 2) + (2x^3 + 6x^2 - 10) + (-13x^3 + 9x^2 - 5) \]

Step 2: Combine Like Terms

To simplify, we combine the coefficients of like terms:

For \(x^3\) terms: \(5 + 2 - 13 = -6\)
For \(x^2\) terms: \(-4 + 6 + 9 = 11\)
For constant terms: \(2 - 10 - 5 = -13\)

Step 3: Write the Simplified Polynomial

The simplified polynomial is: \[ -6x^3 + 11x^2 - 13 \]

Final Answer

The result of adding the polynomials is: \[ \boxed{-6x^3 + 11x^2 - 13} \]

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