Question

1. $18x^{2}+74x+60$

Explanation:

Step1: Factor out GCF of coefficients

The greatest common factor (GCF) of 18, 74, and 60 is 2.
$18x^2 + 74x + 60 = 2(9x^2 + 37x + 30)$

Step2: Factor the quadratic trinomial

Find two numbers that multiply to $9\times30=270$ and add to 37. These numbers are 27 and 10. Split the middle term and factor by grouping:
$9x^2 + 27x + 10x + 30 = 9x(x+3) + 10(x+3) = (9x+10)(x+3)$

Step3: Combine with the factored GCF

Substitute the factored trinomial back into the expression from Step1.
$2(9x+10)(x+3)$

Answer:

$2(9x+10)(x+3)$