The factorization of the trinomial 12x² - 32x - 12, by the use of mid-term factorization method is 4(3x + 1)(x - 3). Hence, option B is the right choice.
How to factor a quadratic expression?
A quadratic expression of the form ax² + bx + c is factored by using the mid-term factorization method, which suggests that b should be broken in such two components that their product = ac. After this, we can factorize using the grouping method.
How to solve the question?
In the question, we are asked to factor the trinomial 12x² - 32x - 12.
As we can see it's a quadratic expression, we will use the mid-term factorization method to factorize it.
On comparing 12x² - 32x - 12 to ax² + bx + c, we can say that a = 12, b = -32, and c = -12.
Now, as per the mid-term factorization method, we will try to break b = -32, in such two numbers that their product = ac = 12*(-12) = -144.
We get this break as -36 and 4. Substituting these in our expression, we get:
12x² - 32x - 12
= 12x² - 36x + 4x -12 {Breaking mid-term}
= 12x(x - 3) + 4(x - 3) {Grouping}
= (12x + 4)(x - 3) {Grouping}
= 4(3x + 1)(x - 3) {Taking common}.
Therefore, the factorization of the trinomial 12x² - 32x - 12, by the use of mid-term factorization method is 4(3x + 1)(x - 3). Hence, option B is the right choice.
Learn more about mid-term factorization at
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