Factorize the quadratic trinomial [tex] x^2 - 9x + 14 [/tex] by the rule:
[tex] ax^2+bx+c=a(x-x_1)(x-x_2), \text{ where } x_1,\ x_2 \text{ are its roots. } [/tex]
1. Find the roots:
[tex] D=(-9)^2-4\cdot 14=81-56=25,\ \sqrt{D}=5,\\
\\ x_1=\dfrac{9-5}{2}=2,\ x_2=\dfrac{9+5}{2}=7. [/tex]
2. Factorize the polynomial:
[tex] x^2 - 9x + 14=(x-2)(x-7). [/tex]
3. Only factor x-2 is given in options, then the correct choice is B.
