the area of a rectangular rug is given by the trinomial r^2-8r-33 use factoring​

Accepted Solution

Hello!The answer is: [tex]r^{2}-8r-33=(r+3)(r-11)[/tex]With:[tex]r=-3\\r=11[/tex]Why?Factoring the quadratic expression we have:We are looking for two possible values that multiplied gives as result -33 and its algebraic sum gives as result -8, so:[tex]r^{2}-8r-33=(r+3)(r-11)[/tex]Also,There are two possible values that make the equation equal to zero: -3 and 11Let's prove by substituting each value:Substituting -3[tex](-3+3)(-3-11)=(0)(-14)=0[/tex]Substituting 11[tex](11+3)(11-11)=(14)(0)=0[/tex]So, there are two possible values for r (area):[tex]r=-3\\r=11[/tex]Have a nice day!