Question

factorise x^2-x-6 using factor theorem

Answer 1

Answer : x = 2 , x = -3

Step-by-step explanation: x^2-x-6

X^2-3x+2x-6

X(x-3) + 2(x-3)

(X+2) (x-3)

Answer 2

Answer:

(x - 3)(x + 2) = 0

Step-by-step explanation:

Given:-  The given polynomial is $x^{2} -x-6$

To Find:- Factorize the given polynomial using Factor theorem.

Solution:-

Factor Theorem is a kind of polynomial remainder theorem which is used to factor the polynomials or to find the roots of the polynomials.

Factor theorem states that if f(x) is a polynomial of degree n that is greater than or equal to 1, and if 'a' is any real number, then (x - a) is a factor of f(x) if and only if f(a) = 0.

Here, the given polynomial is $x^{2} -x-6=0$

⇒ $x^{2} -x-6 =0$

⇒ $x^{2} -(3-2)x-6=0$

⇒ $x^{2} -3x+2x-6=0$

⇒ x(x - 3)+2(x - 3) = 0

⇒ (x - 3)(x + 2) = 0

⇒ x = 3, -2

Therefore (x - 3) and (x + 2) are the factors of the polynomial $x^{2} -x-6$ and 3, -2 are the roots of the given polynomial.

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To know what is a Factor theorem, click here

https://brainly.in/question/1903289

Proof of Factor theorem is available here

https://brainly.in/question/2934137