Question

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.

Answer 1

Sophie factored completely. Carlos did not, because he left an extra term in the factorization that Sophie removed.

Answer 2

$-4x^2 − 10x + 6$

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