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Step 2: Write the polynomial in descending order and use parentheses around like terms.

(3 – 4x + 8x2) + (–6 + 2x – 5x2)

(3-6) + ( – 4x + 2x) + ( 8x2– 5x2)

( 8x2– 5x2) +( – 4x + 2x)+ (3-6)

( – 4x + 2x)+ (3-6) + ( 8x2– 5x2)

(8x2 – 4x +3)+ (– 5x2+ 2x –6)Step 3: Add the like terms identified in Step 2 to simplify the polynomial.

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To simplify the polynomial, we'll combine the like terms identified in Step 2.

Starting from:

\[ (8x^2 - 5x^2) + (-4x + 2x) + (3 - 6) \]

Let's simplify each group of like terms:

  1. For the \(x^2\) terms: \[ 8x^2 - 5x^2 = 3x^2 \]

  2. For the \(x\) terms: \[ -4x + 2x = -2x \]

  3. For the constant terms: \[ 3 - 6 = -3 \]

Now, we combine the simplified terms together in descending order of the degree:

\[ 3x^2 - 2x - 3 \]

Thus, the simplified polynomial is:

\[ 3x^2 - 2x - 3 \]