The model represents x2 – 9x + 14. An algebra tile configuration showing only the Product spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 9 are labeled negative x, and 14 are labeled +. Which is a factor of x2 – 9x + 14? x – 9 x – 2 x + 5 x + 7The answer is x-2

I didn't get all the part with the tiles, but here's the general answer: given a polynomial[tex]p(x)=ax^2+bx+c[/tex]we have that [tex]x-k[/tex] is a factor of [tex]p(x)[/tex] if and only if k is a root of [tex]p(x)[/tex], i.e. if[tex]p(k)=ak^2+bk+c=0[/tex]So, given the polynomial[tex]p(x)=x^2-9x+14[/tex]We can check if [tex]x-9[/tex] is a factor by evaluating [tex]p(9)[/tex]:[tex]p(9)=81-81+14=14\neq 0[/tex]So, [tex]x-9[/tex] is not a factor.Similarly, we can evaluate [tex]p(2),\ p(-5),\ p(-7)[/tex] to check if [tex]x-2,\ x+5,\ x+7[/tex] are factors:[tex]p(2)=4-18+14=0,\quad p(-5)=25+45+14=84\neq 0,\quad p(-7)=49+63+14=126 \neq 0[/tex]So, only [tex]x-2[/tex] is a factor of [tex]x^2-9x+14[/tex]