Factor the trinomal: 3a^2-13a+4

(3a-1)(a-4)

Explanation please?

To factor the trinomial 3a^2 - 13a + 4, we need to find two binomials whose product equals the given trinomial.

Step 1: Multiply the coefficient of the leading term (3) by the constant term (4). In this case, 3 * 4 = 12.

Step 2: Look for two numbers whose sum is equal to the coefficient of the middle term (-13) and whose product is equal to the result of Step 1 (12). In this case, these numbers are -12 and -1 since -12 + (-1) = -13 and (-12) * (-1) = 12.

Step 3: Rewrite the middle term (-13a) using the two numbers found in Step 2 (-12a - 1a).

Now, we can rewrite the trinomial as follows:
3a^2 - 12a - 1a + 4

Step 4: Group the terms into two pairs and factor out the greatest common factor from each pair:
(3a^2 - 12a) + (-1a + 4)
3a(a - 4) - 1(a - 4)

Step 5: Notice that the terms (a - 4) are now common in both pairs. Factor out the common binomial:
(a - 4)(3a - 1)

Therefore, the factored form of the trinomial 3a^2 - 13a + 4 is (a - 4)(3a - 1).