Two students, Carlos and Sophie, factored the trinomial –4x2 − 10x + 6. Sophie factored it as –2(2x − 1)(x + 3) and Carlos factored it as (x + 3)( –4x + 2). Indicate which student factored the trinomial completely and which student did not, and explain why.
Sophie factored completely. Carlos did not, because he left an extra term in the factorization that Sophie removed.
\(-4x^2 − 10x + 6\)
2 is the Greatest common factor . There is negative sign with x^2 so factor out -2
\(-2(2x^2 + 5x - 3)\)
Find out two factors whose sum is +5 and product is -6
\(-2(2x^2 + 6x -1x - 3)\)
\(-2(2x^2 + 6x)(-1x - 3)\)
\(-2(2x(x+3)-1(x + 3))\)
\(-2(2x-1)(x+3)\)
Sophie factored it correctly. Carol forgot to factor completely.
Carol can factor ( –4x + 2) by factoring out -2 from -4x+2