You are simplifying the following: (6x^3 + 2x^2 - 5x - 14) - (-5x^3 + 7x^2 + 2x - 1) The following is step 1. The ___ are the blanks that you need to fill in. Fill in the ___ with the correct sign: 6x^3 ___ 2x^2 ___ 5x ___ 14 ___ 5x^3 ___ 7x^2 ___ 2x ___ 1

Answer 1

To simplify \((6x^3 + 2x^2 - 5x - 14) - (-5x^3 + 7x^2 + 2x - 1)\), we first need to distribute the negative sign across the second polynomial. This means changing the signs of each term in the second polynomial.

Here’s how you would fill in the blanks:

1. The first polynomial is \(6x^3 + 2x^2 - 5x - 14\).
2. Now, we rewrite the second polynomial with the negative sign applied: \(- (-5x^3) = +5x^3\), \(- (7x^2) = -7x^2\), \(- (2x) = -2x\), and \(- (-1) = +1\).

So putting it all together in the step 1 format:

\(6x^3 + 2x^2 - 5x - 14 + 5x^3 - 7x^2 - 2x + 1\)

Thus, the filled-in blanks would be:

6x^3 + 2x^2 - 5x - 14 + 5x^3 - 7x^2 - 2x + 1