Question

Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference. (2 points)%0D%0A %099x2%0D%0A9%0D%0A𝑥%0D%0A2%0D%0A+%09x%09+%0913%0D%0A–%092x2%0D%0A2%0D%0A𝑥%0D%0A2%0D%0A+%0912x%0D%0A12%0D%0A𝑥%0D%0A+%09%0D%0A %09x2%0D%0A𝑥%0D%0A2%0D%0A+%095x%0D%0A5%0D%0A𝑥%0D%0A+%092

Answer 1

To complete the polynomial equation that involves the subtraction of the second expression from the first, we need to structure it properly.

Given the first expression: \[ 9x^2 + 2x + 13 \]

And the second expression: \[ 2x^2 + 12x + 2 \]

We now need to subtract the second expression from the first: \[ (9x^2 + 2x + 13) - (2x^2 + 12x + 2) \]

Distributing the negative sign across the second polynomial yields: \[ 9x^2 + 2x + 13 - 2x^2 - 12x - 2 \]

Now, let's combine like terms:

1. For \(x^2\) terms: \(9x^2 - 2x^2 = 7x^2\)
2. For \(x\) terms: \(2x - 12x = -10x\)
3. For constant terms: \(13 - 2 = 11\)

Putting it all together, the resulting difference is: \[ 7x^2 - 10x + 11 \]

So, the completed polynomial equation showing the subtraction is: \[ 9x^2 + 2x + 13 - (2x^2 + 12x + 2) = 7x^2 - 10x + 11 \]