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)9x^2 + _ x + 13 – 2x^2 + 12x + _ _x2 + 5x + 2

Answer 1

To complete the polynomial equation, we'll first organize the terms clearly.

We have two polynomial expressions:

1. \(9x^2 + bx + 13\) (first expression)
2. \(2x^2 + 12x + cx^2 + 5x + 2\) (second expression)

We need to rewrite the second expression correctly since it seems to have a format error. We’ll assume that the expression is meant to be a polynomial without the extra \(x^2\) term mentioned, focusing on the coefficients instead.

Now, the subtraction looks like this:

\[
(9x^2 + bx + 13) - (2x^2 + 12x + 5x + 2)
\]

We can combine the like terms in the second expression:
\(12x + 5x = 17x\).

Thus, the polynomial we are subtracting is:
\[
2x^2 + 17x + 2
\]

Now we subtract it from the first expression:

\[
(9x^2 + bx + 13) - (2x^2 + 17x + 2)
\]

This results in:
\[
(9x^2 - 2x^2) + (bx - 17x) + (13 - 2)
\]
which simplifies to:
\[
(9 - 2)x^2 + (b - 17)x + (13 - 2)
\]
So we have:
\[
7x^2 + (b - 17)x + 11
\]

Now, we can denote:
- For the first blank \(b - 17\), we can just denote this as: it needs to remain, say \(b = 17 + d\) where \(d\) is what will come from original blanks.

- For the second blank, it is \(11\), as that is the value from subtracting \(13 - 2\).

Finally, we have:
\[
9x^2 + bx + 13 - (2x^2 + 17x + 2) = 7x^2 + (b - 17)x + 11
\]

To answer:
The filled blanks would be \(b=17\) and \(11\), so:

- First blank (coefficient of x): **17**
- Second blank (constant term): **11**
Therefore, your expression reads properly as:
\[
9x^2 + 17x + 13 - (2x^2 + 17x + 2) = 7x^2 + 0x + 11
\]

And directly filling it gives you:
\[
9x^2 + 17x + 13 - 2x^2 + 12x + 11 x^2 + 5x + 2
\]

Answer: **17, 11**