Answer:
The binomial: (x-2) (second option of the list) is a factor of the given trinomial
Step-by-step explanation:
You are looking for two binomial factors of the form; (x+a) and (x+b), with values "a" and "b" such that:
Their product "a times b" results in: "+14" (the numerical term in the initial trinomial [tex]x^2-9x+14[/tex],
and their combining "a+b" results in "-9" (the coefficient in the middle term of the trinomial)
Such number "a" and "b" are: "-2" and "-7".
We can see by multiplying the binomials formed with these numbers:
(x-2) and (x-7) that their product indeed renders the original trinomial:
[tex](x-2) (x-7)= x^2-7x-2x+14=x^2-9x+14[/tex]
therefore, the binomials (x-2) and (x-7) are factors of the given trinomial.
The only one shown among the four possible options is then: (x-2)
