Answer:
(4x-1)(3x-1)
Explanation:
Given the quadratic expression:
[tex]12x^2-7x+1[/tex]To factorize, follow the steps below.
Step 1: Multiply the coefficient of x² and the constant.
[tex]12\times1=12[/tex]Step 2: Find two numbers that multiply to give 12, and add to give the coefficient of x, -7.
• To do this, list the factors of 12: 1,2,3,4,6,12
,• Then select your two numbers by observation.
[tex]\begin{gathered} 4\times3=12 \\ -4-3=-7 \end{gathered}[/tex]Step 3: Rewrite the middle with those numbers.
[tex]12x^2-7x+1=12x^2-4x-3x+1[/tex]Step 4: Factor the first two and last two terms separately.
Ensure that the expression in the brackets is the same.
[tex]\begin{gathered} =4x(3x-1)-1(3x-1) \\ =(4x-1)(3x-1) \end{gathered}[/tex]The factored form is (4x-1)(3x-1).
