Question

1. $3x^{2}+10x + 8 = 0$

Explanation:

Step1: Factor the quadratic equation

We need to factor \(3x^{2}+10x + 8 = 0\). We look for two numbers that multiply to \(3\times8 = 24\) and add up to \(10\). The numbers are \(6\) and \(4\). So we rewrite the middle term:
\(3x^{2}+6x + 4x+8 = 0\)

Step2: Group and factor

Group the first two terms and the last two terms:
\((3x^{2}+6x)+(4x + 8)=0\)
Factor out the common factors from each group:
\(3x(x + 2)+4(x + 2)=0\)
Now factor out \((x + 2)\):
\((3x + 4)(x + 2)=0\)

Step3: Solve for x

Set each factor equal to zero:
\(3x+4 = 0\) or \(x + 2=0\)
For \(3x+4 = 0\), we get \(3x=-4\), so \(x=-\frac{4}{3}\)
For \(x + 2=0\), we get \(x=-2\)

Answer:

\(x = - 2\) or \(x=-\frac{4}{3}\)