Question
Which of the following is/are the irreducible factor(s) of 3m2+9m+6?
Answer: Option A
:
A, B, and D
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:
A, B, and D
Given, the expression is
3m2+9m+6.
Taking 3 common from the above expression, we get
3(m2+3m+2) ...(i)
Now comparing m2+3m+2 with the identity x2+(a+b)x+ab.
We note that,
(a+b)=3 and ab=2.
So,
2+1=3 and (2)(1)=2
Hence,
m2+3m+2
=m2+2m+m+2
=m(m+2)+1(m+2)
=(m+2)(m+1)
Now from (i), we get
⇒3m2+9m+6=3(m2+3m+2)=3(m+2)(m+1)
Therefore,
3, (m+2) and (m+1) are the 3 irreducible factors of the given expression.
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