Question

1. $4x^{2}+24x+27$

Explanation:

Step1: Split middle term

Find two numbers that multiply to $4\times27=108$ and add to 24: 6 and 18.
Rewrite the expression: $4x^2 + 6x + 18x + 27$

Step2: Group and factor pairs

Group first/second and third/fourth terms: $(4x^2 + 6x) + (18x + 27)$
Factor out GCF from each group: $2x(2x + 3) + 9(2x + 3)$

Step3: Factor common binomial

Factor out $(2x+3)$ from both terms: $(2x + 3)(2x + 9)$

Answer:

$(2x + 3)(2x + 9)$