Question

operations with polynomials 2
polynomial 1: $5x^2 - 6x + 5$
polynomial 2: $2x^2 - 12x + 8$

Explanation:

Assuming the operation is addition (since the problem title is "Operations with Polynomials" and no specific operation is given, addition is a common operation with polynomials):

Step1: Identify like terms

Polynomial 1: \(5x^2 - 6x + 5\)
Polynomial 2: \(2x^2 - 12x + 8\)
Like terms: \(5x^2\) and \(2x^2\); \(-6x\) and \(-12x\); \(5\) and \(8\)

Step2: Add the coefficients of like terms

For \(x^2\) terms: \(5x^2 + 2x^2 = (5 + 2)x^2 = 7x^2\)
For \(x\) terms: \(-6x + (-12x) = (-6 - 12)x = -18x\)
For constant terms: \(5 + 8 = 13\)

Step3: Combine the results

The sum of the two polynomials is \(7x^2 - 18x + 13\)

If the operation was subtraction (Polynomial 1 - Polynomial 2):

Step1: Distribute the negative sign

Polynomial 1: \(5x^2 - 6x + 5\)
Polynomial 2: \(2x^2 - 12x + 8\)
\(5x^2 - 6x + 5 - (2x^2 - 12x + 8) = 5x^2 - 6x + 5 - 2x^2 + 12x - 8\)

Step2: Combine like terms

For \(x^2\) terms: \(5x^2 - 2x^2 = 3x^2\)
For \(x\) terms: \(-6x + 12x = 6x\)
For constant terms: \(5 - 8 = -3\)

Step3: Combine the results

The difference is \(3x^2 + 6x - 3\)

Since the problem didn't specify the operation, but if we assume addition (a common first operation with polynomials):

Answer:

If adding: \(7x^2 - 18x + 13\)
If subtracting: \(3x^2 + 6x - 3\)

(Please specify the operation if this is not what you wanted, e.g., multiplication, division, etc.)