Question

1. $30a^2 - a - 1$

Explanation:

Step1: Find product of first/last terms

$30 \times (-1) = -30$

Step2: Split middle term

Find two factors of -30 that sum to -1: $5$ and $-6$.
Rewrite the expression: $30a^2 +5a -6a -1$

Step3: Factor by grouping

Group terms: $(30a^2 +5a) + (-6a -1)$
Factor out GCFs: $5a(6a +1) -1(6a +1)$

Step4: Extract common binomial

$(6a +1)(5a -1)$

Answer:

$(6a + 1)(5a - 1)$