Q 87E - Intermediate Algebra

Question

In the following exercises, factor each trinomial of the form 

$$\begin{gathered} x^2+bxy+c{y}^2 \\ {m}^2-5mn+30n^2 \end{gathered}$$

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  $m^2-5mn+30n^2$

Step 2. Writing factors as two binomial with first term m and second term n.

The factors should be written as two binomials with first term m and second term n. 

$(m n)(m n)$

The product of the two numbers is 30 ,and their sum is 5. Because the third term sign is negative, the sum seems to be a difference.

$\begin{array}{ccccc}\mathrm{Factors}& 30& 15& 10& 6\\ & 1& 2& 3& 5\\ \mathrm{Difference}& 29& 13& 7& 1\end{array}$

There are no factors pair that sum is 5. The given trinomial is prime.