To find the missing terms in the polynomial equation, we start with the subtraction of the second expression from the first. We have the following two expressions:
- \(9x^2 + __x + 13\)
- \(-2x^2 + 12x + __\)
We want to subtract the second expression from the first:
\[ (9x^2 + __x + 13) - (-2x^2 + 12x + __) = __x^2 + 5x + 2 \]
When we simplify the left side, we get:
\[ 9x^2 + __x + 13 + 2x^2 - 12x - __ \]
This simplifies to:
\[ (9x^2 + 2x^2) + (__x - 12x) + (13 - __) \]
This results in:
\[ (11x^2) + (__ - 12)x + (13 - __) \]
Now, we want this to equal the expression on the right side:
\[ __x^2 + 5x + 2 \]
From this, we can set up equations based on the coefficients:
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For \(x^2\): \[ 11 = __ \quad \Rightarrow \quad __ = 11 \]
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For \(x\): \[ __ - 12 = 5 \quad \Rightarrow \quad __ = 5 + 12 = 17 \]
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For the constant term: \[ 13 - __ = 2 \quad \Rightarrow \quad __ = 13 - 2 = 11 \]
Putting it all together, we have:
- The missing coefficient for \(x\) in the first expression is 17.
- The missing term in the second expression is 11.
- The missing coefficient for the constant term in the second expression is 11.
So, the completed polynomial equation is:
\[ 9x^2 + 17x + 13 - (-2x^2 + 12x + 11) = 11x^2 + 5x + 2 \]
Final answers:
- 17 for the \(x\) term in the first expression.
- 11 for the constant term in the second expression.
- 11 for the \(x^2\) term in the resulting difference.
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