To complete the polynomial equation, we'll first organize the terms clearly.
We have two polynomial expressions:
- \(9x^2 + bx + 13\) (first expression)
- \(2x^2 + 12x + cx^2 + 5x + 2\) (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:
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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.
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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
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