Answer
Fill the blank with $x-2y.$
Work Step by Step
$ax^{2}+bx+c=(F_{1}x+L_{1})(F_{2}x+L_{2})$
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 $b$
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The product of Firsts is $5x^{2} $
... for this to work, $F_{2}$ must be $ 1x=x$
The product of Lasts is $-4y^{2}$
... for this to work, the last term in the second parentheses should be $-2y.$
Proposed factorization: $(5x+2y)(x-2y)$
The sum of Outside product and Inside product is $-8y$
$5(-2y)+(2y)(1)= -8y\qquad ... (OK)$
Fill the blank with $x-2y.$
