Question

1. $10a^{2}-29a-72$

Explanation:

Step1: Find pair for AC method

We use the AC method for quadratic $ax^2+bx+c$. Here, $a=10$, $b=-29$, $c=-72$. Calculate $ac=10\times(-72)=-720$. Find two numbers that multiply to $-720$ and add to $-29$: these numbers are $-45$ and $16$.

Step2: Split middle term

Rewrite the quadratic by splitting the middle term using the two numbers:
$10a^2 - 45a + 16a - 72$

Step3: Factor by grouping

Group the first two and last two terms, then factor out the GCF from each group:
$5a(2a - 9) + 8(2a - 9)$

Step4: Factor out common binomial

Factor out the shared binomial $(2a - 9)$:
$(5a + 8)(2a - 9)$

Answer:

$(5a + 8)(2a - 9)$