Question

How Would I Factor the Trinomial
3y^2 + 7y - 20
Using the Tic-tac-toe or box method?

Answer 1

`ay^2 + by + c = a(y -y_1)(y - y_2)`


`y_(1,2) = (-b \pm √(b^2-4ac))/(2a)\\\\y_(1,2) = ( -7 \pm √( 7 ^2 - 4 \cdot 3 \cdot (-20)) )/( 2 \cdot 3 )\\\\y_(1,2) = ( -7 \pm √( 289 ) )/( 6 )\\\\\\y_1 = ( -7~+~√( 289 ) )/( 6 ) = ( 5 )/( 3 )\\\\y_2 = ( -7~-~√( 289 ) )/( 6 ) = -4`


`3y^(2)+7y-20 = 3 \left(y - \left( -4 \right)\right)\left(y - ( 5 )/( 3 ) \right)\\\\3y^(2)+7y-20 = 3 \left(y + 4 \right)\left(y - ( 5 )/( 3 )\right)\\\\\\3y^(2)+7y-20 = ( y+4 )( 3y-5 )`