Question

In the following exercises, factor each trinomial of the form $x^2+bxy+c{y}^2$

$u^2-8uv-24v^2$

Short answer

The factorization of the expression$u^2-8uv-24v^2$is not factorable.

Step-by-step solution

Step 1. Given information

Given expression is$u^2-8uv-24v^2$

Step 2. Find the last terms of the trinomials.

The factors of the expression:

Factors of -24	Sum of factors
8, -3	8 + (-3) = 5
-8, 3	-8 + (3) = -5
6, -4	6 + (-4) = 2
-6, 4	-6 + (4) = -2
12, -2	12 + (-2) = 10
-12, 2	-12 + 2 = -10
-24, 1	-24 + 1 = -23
-1, 24	-1 + 24 = 23

Step 3. Factorization

Among the pair of numbers, there are no pairs with the sum of $-8$

The given expression$u^2-8uv-24v^2$cannot be simplified further.