The problem asks us to factor the polynomial $2a^2 - 7a + 5$ using the grouping number method.

1. Problem Description

The problem asks us to factor the polynomial $2a^2 - 7a + 5$ using the grouping number method.

2. Solution Steps

First, we need to find two numbers that multiply to $2 \cdot 5 = 10$ and add up to $-7$.

The numbers are $-2$ and $-5$, since $(-2) \cdot (-5) = 10$ and $(-2) + (-5) = -7$.

Now we rewrite the middle term $-7a$ as $-2a - 5a$.

So, we have $2a^2 - 7a + 5 = 2a^2 - 2a - 5a + 5$.

Next, we group the terms in pairs: $(2a^2 - 2a) + (-5a + 5)$.

Now, we factor out the greatest common factor (GCF) from each pair.

From the first pair, we can factor out $2a$: $2a(a - 1)$.

From the second pair, we can factor out $-5$: $-5(a - 1)$.

So, we have $2a(a - 1) - 5(a - 1)$.

Now, we factor out the common factor $(a - 1)$ from both terms: $(a - 1)(2a - 5)$.

3. Final Answer

$(a-1)(2a-5)$