Problem

For the partially complete factorization, find the other binomial which will complete the factorization.
\[
a^{2}+7 a-18=(a+9)(
\]

Answer

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Answer

Final Answer: The other binomial which will complete the factorization is \(\boxed{(a - 2)}\).

Steps

Step 1 :The given expression is a quadratic equation in the form of \(ax^2 + bx + c\). The factorization of a quadratic equation is given by \((x - p)(x - q)\) where \(p\) and \(q\) are the roots of the equation. In this case, we are given one of the factors as \((a + 9)\), so we need to find the other factor.

Step 2 :To find the other factor, we can use the formula for the roots of a quadratic equation, which is \(-b \pm \sqrt{b^2 - 4ac} \over 2a\). However, since we already have one of the roots, we can simply divide the quadratic equation by the given factor to find the other root.

Step 3 :By dividing the quadratic equation by the given factor, we find the other factor to be \(a - 2\).

Step 4 :Final Answer: The other binomial which will complete the factorization is \(\boxed{(a - 2)}\).

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