How can I simplify the polynomial 8x² + 8x + 2 – 5x to express it in the form 8x² + gx + h, and what are the exact values of g and h?

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To simplify the polynomial 8x² + 8x + 2 – 5x, we first need to combine like terms. Let’s break it down step by step:

1. Start with the original polynomial:

8x² + 8x + 2 – 5x

2. Combine the linear terms (the terms containing x):

8x + 2 – 5x = (8 – 5)x + 2 = 3x + 2

3. Now, plug this back into the polynomial:

8x² + 3x + 2

4. Now, we can rewrite the polynomial in the form 8x² + gx + h. In this case, we can see that:

  • g = 3
  • h = 2

So, the simplified polynomial is 8x² + 3x + 2, and the values of g and h are:

  • g = 3
  • h = 2

This final form is clear and organized, making it easier to work with for any further calculations or evaluations.

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