## Introductory Algebra for College Students (7th Edition)

Fill the blank with $-3.$
$ax^{2}+bx+c=(F_{1}x+L_{1})(F_{2}x+L_{2})$ FOIL: (F)irst, (L)ast...Outers: $F_{1}$and $L_{2},$ Inners=$L_{1}$ and $F_{2}$ The product of Firsts is $ax^{2}$ The product of Lasts is $c$ The sum of Outside product and Inside product is $b$ --- The product of Firsts is $8x^{2}\qquad(OK)$ The product of Lasts is $-3$ ... for this to work, the last term in the second parentheses should be $-3.$ Proposed factorization: $(4x+1)(2x-3)$ The sum of Outside product and Inside product is $-10$ If $L_{2}=-3, \qquad 4(-3)+1*2=-10\qquad ... (OK)$ Fill the blank with $-3.$