Hello i have a doubt in splitting of middle terms
for example take 3x2 +13x+4
= 3x(x+4) + 1(x+4)
how did we get 3x(x+4) and 1(x+4)???
To factorize any polynomial,
Step (1) : Multiply the quadratic term and constant term.
Step (2) : then write all the factors of result in pairs, which you get in step (1).
Step (3) : from all the factors, find the pair that adds to produce the coefficient of linear term.
Step (4) : Break up the linear terms into two terms, which you get in step (3).
Step (5) : Group the four terms into two sets.
Step (6) : find the H.C.F. from each set and factor it out.
For Example : 3x2 + 13x + 4
(1) 3x2 × 4 = 12x2
(2) 1x and 12x
(3) + x + 12x = 13x, linear term is 13x and we will take x and 12x
(4) 3x2 + x + 12x + 4 or 3x2 + 12x + x + 4
(5) (3x2 + x) + (12x + 4) or (3x2 + 12x) + (x + 4)
(6) x(3x + 1) + 4(3x + 1) or 3x(x + 4) + 1(x + 4)
= (x + 4)(3x + 1) or (3x + 1)(x + 4)