Question

the area of a rectangle is given by the trinomial 10ײ - 31x-14. The length of the rectangle is 5x+2. What is the expression for the width of the field.

Answer 1

$10x^2 - 31x-14=10x^2+4x-35x-14=2x(5x+2)-7(5x+2)=\\\\=(5x+2)(2x-7)\\\\D:\ \ 5x+2>0\ \ \ and\ \ \ \ \ 2x-7>0\\.\ \ \ \ \ \ 5x>-2\ \ \ \ \ \ and\ \ \ \ \ 2x>7\\.\ \ \ \ \ \ \ x>-\frac{2}{5}\ \ \ \ \ \ and\ \ \ \ \ \ x>3 \frac{1}{2} \\\\D=(3 \frac{1}{2};\ +\infty)\\\\Ans.\ \ The\ width\ is\ \ \ \ 2x-7$