Question

1. 6n² + 5n - 6

Explanation:

Step1: Multiply coefficients

Multiply the coefficient of $n^{2}$ (which is 6) and the constant - 6. We get $6\times(-6)= - 36$. We need to find two numbers that multiply to - 36 and add up to the coefficient of $n$ (which is 5).

Step2: Find factor pair

The factor - pair of - 36 that adds up to 5 is 9 and - 4 since $9\times(-4)=-36$ and $9+( - 4)=5$.

Step3: Rewrite middle term

Rewrite the middle term $5n$ as $9n-4n$. So, $6n^{2}+5n - 6=6n^{2}+9n-4n - 6$.

Step4: Group terms

Group the terms: $(6n^{2}+9n)-(4n + 6)$.

Step5: Factor out GCF from each group

From the first group $6n^{2}+9n$, the greatest common factor (GCF) is 3n. Factoring out 3n gives $3n(2n + 3)$. From the second group $4n + 6$, the GCF is 2. Factoring out 2 gives $2(2n+3)$.

Step6: Factor out common binomial

We have $3n(2n + 3)-2(2n + 3)$. Factoring out the common binomial $(2n + 3)$ gives $(2n + 3)(3n-2)$.

Answer:

$(2n + 3)(3n-2)$