Question

1. factor the following completely

a. $3x^2 + 10x + 8 =$

Explanation:

Step1: Identify \(a\), \(b\), \(c\)

For \(3x^2 + 10x + 8\), \(a = 3\), \(b = 10\), \(c = 8\).

Step2: Find two numbers

Find two numbers that multiply to \(a\times c=3\times8 = 24\) and add to \(b = 10\). The numbers are \(6\) and \(4\) (since \(6\times4 = 24\) and \(6 + 4 = 10\)).

Step3: Split the middle term

Rewrite \(10x\) as \(6x + 4x\): \(3x^2+6x + 4x + 8\).

Step4: Group and factor

Group the first two and last two terms: \((3x^2 + 6x)+(4x + 8)\). Factor out the GCF from each group: \(3x(x + 2)+4(x + 2)\). Then factor out \((x + 2)\): \((3x + 4)(x + 2)\).

Answer:

\((3x + 4)(x + 2)\)