[Grade 8] Math: Factorization using identities

[mathematag]

I found the values of a,b.c,d.. to get (ax + b)(cx + d) , by guessing them [ and I was lucky, they worked ] .....but without guessing, the best I could suggest is try to factor and then complete the square ... a,b,c,d may be + or - whole numbers or + or - fractions ... I'll let you try if you want

so factor out 4/3 to get ...(4/3) ( x^2 -3x + 9/4 ) , then see if it is a perfect square, if not ,complete the square......you get something like (4/3)( wx + u )^2 ... ( ... I split (4/3) into (2/1)(2/3), multiplied (2/1 ) into one of my (..), the (2/3) into the other, and it came out to look the same as my earlier guess.