Factorization of 12x2−7x+1 will be ____.

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Detailed Solution

12x2−7x+1
First, we will split the middle term of the quadratic equation 12x2−7x+1 into two new terms. We have to split the terms in such a way that the coefficients of the two terms are the factors of the term obtained from the multiplication of the coefficient of x2 and the constant term.
Multiplication of the coefficient of x2 and the constant term =12
The factors of 12 are 4 and 3. Therefore, we will split the middle term as;
⇒ 12x2−7x+1 = 12x2−4x−3x+1
Now, we will factorize the first two terms and last two terms separately.
⇒ 12x2−7x+1 = 4x(3x−1) − (3x−1)
We can see that both new terms have a common factor.
Therefore,
⇒ 12x2−7x+1 = (4x−1)(3x−1)
Hence, the factorization of 12x2−7x+1 is (4x−1)(3x−1) .

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