Q 86E - Intermediate Algebra

Question

In the following exercises, factor each trinomial of the form  $$\begin{gathered} x^2+bxy+c{y}^2 \\ {u}^2-8uv-24v^2 \end{gathered}$$

Step-by-Step Solution

Answer

The trinomial is prime. Hence there is no factors for the equation. 

Step 1. Given information

The given equation is  $u^2-8uv-24v^2$.

Step 2. Writing factors as two binomial with first term u and second term v.

The factors should be written as two binomials with first term u and second term v. 

$(u v)(u v)$

The product of the two numbers is 24, and their sum is 8. Because the third term sign is negative, the sum seems to be a difference.

$\left[\begin{array}{ccc}\mathrm{Factors}& 24& 12 8\\ & 1& 2 3\\ \mathrm{Difference}& 23& 10 5\end{array}\right]$

There are no factors pair that sum is 8. The given trinomial is prime.