Let's start by analyzing the first equation given:
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Equation to match: \[ y = x^2 - 1x - 20 \]
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Factored form: \[ y = (x + 8)(x + 11) \]
Now we will expand the factored form \(y = (x + 8)(x + 11)\):
\[ y = x^2 + 11x + 8x + 88 \] \[ y = x^2 + 19x + 88 \]
Next, we can simplify the original equation \(y = x^2 - 1x - 20\) to confirm if it is equivalent to the expanded terms.
Let's set the right-hand side of the original equation equal to zero and factor it:
To factor \(x^2 - 1x - 20\), we look for two numbers that multiply to \(-20\) (the constant term) and add to \(-1\) (the coefficient of \(x\)). These numbers are \(4\) and \(-5\):
\[ y = (x - 5)(x + 4) \]
However, this does not match with the original factored form \(y = (x + 8)(x + 11)\).
So we can also calculate both polynomial forms.
Comparing both:
The right expanded form of \( (x + 8)(x + 11) = x^2 + 19x + 88 \) matches one of the options.
In summary:
- The equivalent of \(y = (x + 8)(x + 11)\) is: \[ y = x^2 + 19x + 88 \]
Thus, the match is:
\[ y = x^2 - 1x - 20 \text{ does not match any of the options.} \] \[ y = (x + 8)(x + 11) \text{ matches with } y = x^2 + 19x + 88. \]
So the only matched option is: \[ y = x^2 + 19x + 88 \]