Step 3: Add the like terms identified in Step 2 to simplify the polynomial.

(3x – 5 – 7x2) – (–2 + 6x2 – 5x)

1 answer

To simplify the given polynomial expression:

\[ (3x - 5 - 7x^2) - (-2 + 6x^2 - 5x) \]

we need to first distribute the negative sign across the second polynomial:

\[ (3x - 5 - 7x^2) + (2 - 6x^2 + 5x) \]

Now, we can combine like terms. First, let's group the terms by their degrees:

  • For \(x^2\) terms: \(-7x^2 + (-6x^2) = -7x^2 - 6x^2 = -13x^2\)
  • For \(x\) terms: \(3x + 5x = 8x\)
  • For constant terms: \(-5 + 2 = -3\)

Putting it all together, we combine the results:

\[ -13x^2 + 8x - 3 \]

Thus, the simplified form of the polynomial is:

\[ -13x^2 + 8x - 3 \]