In the following exercises, factor each expression.

m2-31mn+30n2

Short Answer

Expert verified

The factorization ofm2-31mn+30n2is,(m-30n)(m-1n).

Step by step solution

01

Step 1. Given information  

Given expression ism2-31mn+30n2.

02

Step 2. Find the last terms of the trinomials   

Write the factors as trinomials, min the first term of each binomial and nin the second term.

(m_n)(m_n)

Find the numbers that multiply to 30and add to -31.

Factors of 30Sum of factors
-1, -30-1 + (-30) = -31*
-2, -15-2 + (-15) = -17
-3, -10-3 + (-10) = -13
-5, -6-5 + (-6) = -11
03

Step 3. Factorization 

use-30and -1 as the last terms of the coefficents.

m2-31mn+30n2=(m-30n)(m-1n)

04

Step 4. Check  

(m-30n)(m-1n)=m2-30mn-1mn+30mn2=m2-31mn+30n2

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