Question

1. factor: $9x^2 + 3x - 2$

Explanation:

Step1: Identify coefficients and constant

We have the quadratic expression \(9x^2 + 3x - 2\). Here, \(a = 9\), \(b = 3\), \(c=- 2\).

Step2: Multiply \(a\) and \(c\)

Calculate \(a\times c=9\times(-2)= - 18\).

Step3: Find two numbers

We need two numbers that multiply to \(-18\) and add up to \(b = 3\). The numbers are \(6\) and \(- 3\) since \(6\times(-3)=-18\) and \(6+( - 3)=3\).

Step4: Rewrite the middle term

Rewrite the middle term using these two numbers: \(9x^2+6x - 3x - 2\).

Step5: Group and factor

Group the first two terms and the last two terms: \((9x^2 + 6x)+(-3x - 2)\). Factor out the greatest common factor from each group: \(3x(3x + 2)-1(3x + 2)\).

Step6: Factor out the common binomial

Factor out the common binomial \((3x + 2)\): \((3x + 2)(3x - 1)\).

Answer:

\((3x + 2)(3x - 1)\)