Question

# Which of the following is/are the irreducible factor(s) of 3m2+9m+6?

A

3

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B

m+2

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C

m+3

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D

m+1

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Solution

## The correct options are A 3 B m+2 D m+1 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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