Question

Factor completely x2 − 7x + 18

Prime
(x − 9)(x − 2)
(x − 9)(x + 2)
(x + 9)(x + 2)

Answer 1

x2 − 7x + 18
is prime

there is no way you can make two numbers multiply to get positive 18 and add to get negative 7

(x − 9)(x − 2) = x^2 - 11x + 18
(x − 9)(x + 2) = x^2 -7x - 18
(x + 9)(x + 2) = x^2 +11x + 18

Answer 2

Answer:

The factorization of the given expression is not possible.

         Hence, the option that holds true is:

                              Prime.

Step-by-step explanation:

We are given a polynomial expression in terms of variable x as:

                             $x^2-7x+18$

It is a prime expression.

Since we could not factorize our polynomial as the expression do not have any integer roots.

(

Since the roots of the equation is calculated by the quadratic formula:

$x=\dfrac{-(-7)\pm \sqrt{(-7)^2-4\times 1\times 18}}{2\times 1}\\\\\\x=\dfrac{7\pm \sqrt{-23}}{2}\\\\\\x=\dfrac{7\pm \sqrt{23}i}{2}$

)

so it could not be expressed as a product of two linear factors.

           Hence, the answer is:

                     Prime