Question

factor.
$15x^{2}+37x + 18$

Explanation:

Step1: Find two numbers for ac

For the quadratic \(15x^{2}+37x + 18\), \(a = 15\), \(b=37\), \(c = 18\). Calculate \(ac=15\times18 = 270\). We need two numbers that multiply to \(270\) and add to \(37\). The numbers are \(27\) and \(10\) (since \(27\times10 = 270\) and \(27 + 10=37\)).

Step2: Split the middle term

Rewrite the middle term using these numbers: \(15x^{2}+27x + 10x+18\).

Step3: Group and factor

Group the first two and last two terms: \((15x^{2}+27x)+(10x + 18)\). Factor out the GCF from each group: \(3x(5x + 9)+2(5x + 9)\).

Step4: Factor out the common binomial

Now factor out \((5x + 9)\) from both terms: \((3x + 2)(5x + 9)\).

Answer:

\((3x + 2)(5x + 9)\)