Question

6. Which are the factors of x2 - 5x - 6?
(1) (x + 3)(x + 2) (2) (x-6)(x + 1)
(3) (x + 6) (x - 1)
(4) (x - 3)(x - 2)​

Answer 1

Answer:

Given equation

x2 + 5x + 6

Let us try factorizing this polynomial using splitting the middle term method.

Factoring polynomials by splitting the middle term:

We need to find two numbers ‘a’ and ‘b’ such that a + b =5 and ab = 6.

On solving this we obtain, a = 3 and b = 2

Thus, the above expression can be written as:

x2 + 5x + 6

= x2 + 3x + 2x + 6

= x(x + 3) + 2(x + 3)

= (x + 3)(x + 2)

Thus, x+3 and x+2 are the factors of the polynomial x2 + 5x + 6.