Question

question
factor the trinomial:
$3x^{2}+23x + 30$

Explanation:

Step1: Multiply leading - coefficient and constant

Multiply the leading coefficient \(a = 3\) and the constant \(c=30\). So \(a\times c=3\times30 = 90\).

Step2: Find two numbers

Find two numbers that multiply to \(90\) and add up to the middle - coefficient \(b = 23\). The numbers are \(18\) and \(5\) since \(18\times5=90\) and \(18 + 5=23\).

Step3: Rewrite the middle term

Rewrite the trinomial as \(3x^{2}+18x + 5x+30\).

Step4: Group the terms

Group the terms: \((3x^{2}+18x)+(5x + 30)\).

Step5: Factor out the GCF from each group

Factor out the greatest common factor (GCF) from each group. From the first group \(3x^{2}+18x\), the GCF is \(3x\), so \(3x^{2}+18x=3x(x + 6)\). From the second group \(5x + 30\), the GCF is \(5\), so \(5x + 30=5(x + 6)\).

Step6: Factor out the common binomial factor

Factor out the common binomial factor \((x + 6)\): \(3x(x + 6)+5(x + 6)=(3x + 5)(x+6)\).

Answer:

\((3x + 5)(x + 6)\)