Q. 363 - Intermediate Algebra

Question

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

$m^2-5mn+30n^2$

Step-by-Step Solution

Answer

There are no factors for the polynomial $m^2-5mn+30n^2$ . And it is prime.

Step 1. Given

The trinomial is $m^2-5mn+30n^2$

To find the factors of the trinomial.

Step 2. Write binomial with first term m and second term n

The binomial contains $m$ in the each term and $n$ in the second term.

The last term of the trinomial is positive, so the factors must have negative signs.

$m^2-5mn+30n^2=(m- n)(m- n)$

Step 3. Find numbers multiply to 30 and add to - 5

Find the numbers multiply to $30$ and add to $-5$

Factors of $30$	Sum of factors
$-1,-30$	$-31$
$-2,-15$	$-17$
$-3,-10$	$-13$
$-5,-6$	$-11$

Step 4. Find the factors

There is no factor that will multiply to $30$ and add to $-5$.

There are no factor pair that sum is $-5$.

So the trinomial is prime.