Question

Consider that the roots of a cubic equation with integral coefficients are 1, −2, and 3.

Which choice is a factor of the cubic equation?
A) x + 2
B) x + 1
C) x + 3
D) x − 4

Answer 1

Answer: The correct option is (A) x + 2.

Step-by-step explanation: We are given that 1, -2 and 3 are the roots of a cubic equation with integral coefficients.

We are to select the choice that is a factor of the given cubic equation.

Factor theorem : If x = a is a root of a polynomial equation f(x) = 0, then (x - a) is a factor of f(x).

Since x = 1, -2 and 3 are the roots of the given equation, so by Factor theorem, we get

(x - 1), (x + 2) and (x - 3) are the factors of the given polynomial equation.

Since (x - 1) ans (x - 3) are not given in the options, so the correct option is (x + 2).

Thus, option (A) is CORRECT.

Answer 2

The answer is option A) X + 2

Explanation:

Any polynomial of order n can be expressed in terms of their roots in factors of the form

(x-a)(x-b)(x-c)(x-d)....... = 0

Where a,b,c,d,... are the roots of the polynomial

In the example shown

(x+2) = (x-(-2))

And -2 happens to be the root of the polynomial in question