Factorization of 3p2−24p+36 will be ____.

# Factorization of 3p2−24p+36 will be ____.

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### Solution:

We are given an equation, which we have been asked to factorize.
But first, we need to make sure that the equation is in the form of x2−(a+b)x+ab. In the equation that has been given to us, p2  has a coefficient with which is not required. So, we will take the common coefficient of p2 from the entire equation.
⇒3p2−24p+36
Now, we will take the common coefficient of p2.
⇒3(p2−8p+12)
Now, we have to find 2 such numbers which will give us 8 on being added and 12 on being multiplied. Two such numbers are 6 and 2. On simplifying we will get,
⇒3[p2−(6+2)p+(6×2)]
We know the identity: x2−(a+b)x+ab=(x−a)(x−b)
As we can see, a=6,b=2
Putting in the identity, we get –
⇒3(p−6)(p−2)
Hence, the factors of 3p2−24p+36 are (p−6) and (p−2).

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