Split the middle term(term with x) in such a manner so that the product of those parts is equal to the product of term with x² and constant. Here, those parts are 12 & 12 as 12*12 = 9*16.
=> 9x² - 24x + 16
=> 9x² - (12 + 12)x + 16
=> 9x² - 12x - 12x + 16
=> 3x(3x - 4) - 4(3x - 4)
=> (3x - 4)(3x - 4)
Method 2
=> 9x² - 24x + 16
=> (3x)² - 2(3x*4) + 4²
=> (3x - 4)²
=> (3x - 4)(3x - 4)
Method 3
In case if you can't find the factors of the middle term.
Say f(x) = 0, find the zeroes using quadratic formula. Zeroes of this eqⁿ are [-(-24) ± √24²-4(9)(16)] / 2(9) = 4/3 & 4/3
For this,we need to know what's Middle splitting method
In order to factorize x² + bx + c we have to find numbers p and q such that p + q = b and pq = c. After finding p and q, we split the middle term in the quadratic as <em><u>px + qx and</u></em> get desired factors by grouping the terms.
