What will be the factorization of p2+6p+8 ?

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(P+2)(P-2)

(P+4)(2P-2)

(2P+4)(P+2)

(P+4)(P+2)

answer is D.

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Detailed Solution

Step 1: The given equation is p2+6p+8. This is a quadratic equation. Here, the coefficient of p2 is 1, and the coefficient of p is 6, 8 is a constant term. In this expression, the term 8 is not a perfect square.
Step 2: They however seem to be the type of (p+a)(p+b)=p2+(a+b)p+ab. We have to look at the coefficient of p and a constant term. If we compare the right-hand side of identity p2+(a+b)p+ab with p2+6p+8 . We find ab = 8 and a+b = 6.
From this, we must obtain a and b . the factors will be (p+a)(p+b). If ab = 8 it means that a and b are factors of 8. Let us try a = 8 and b = 1
For these values a+b = 9 not 6. This is incorrect.
Let us try a = 4 and b = 2 for these values a+b = 6 this is correct .
So, the given expression can be written as p2+(4+2)p+4×2.
So, we get the factorization form of the given expression then (p+4)(p+2).
So, option 4 is correct.

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