Question

1. what is the factored form of the expression $6x^2 - 5x - 21$?

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(6\times(-21)= -126\) and add up to \(-5\). The numbers are \(-14\) and \(9\) since \(-14\times9 = -126\) and \(-14 + 9=-5\).

Step2: Rewrite the middle term

Rewrite the expression \(6x^{2}-5x - 21\) as \(6x^{2}+9x-14x - 21\).

Step3: Group and factor

Group the first two terms and the last two terms: \((6x^{2}+9x)+(-14x - 21)\). Factor out the greatest common factor from each group: \(3x(2x + 3)-7(2x + 3)\).

Step4: Factor out the common binomial

Factor out the common binomial \((2x + 3)\) to get \((3x - 7)(2x + 3)\).

Answer:

\((3x - 7)(2x + 3)\)