# What would be the most efficient step to suggest to

What would be the most efficient step to suggest to a student attempting to complete this problem?
Factor:
${x}^{2}\left(2a+5\right)x+\left({a}^{2}+5a+6\right)$
a)Distribute (2a+5)
b)Factor in the form (x+c)(x+d)
c)Simplify and group terms with a
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Step 1
Go through the available options to know the correct answer.
(a) Distribute (2a+5).
${x}^{2}+\left(2a+5\right)x+\left({a}^{2}+5a+6\right)={x}^{2}+2ax+5x+{a}^{2}+5a+6$
This step is not efficient to factor the polynomial.
(b) Factorization in the form of (x+c)(x+d) is also not possible.
Step 2
(c) Simplify and group terms with a.
${x}^{2}+\left(2a+5\right)x+\left({a}^{2}+5a+6\right)={x}^{2}+2ax+5x+{a}^{2}+5a+6$
$={x}^{2}+2ax+{a}^{2}+5a+5x+6$
$={x}^{2}+a\left(2x+a+5\right)+5x+6$
This is also not efficient.
Since the function is in simplified form, so the correct option is (d), that is this is not factorable.

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