Question

$factoize \: {x}^{2} - x - 6$
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Answer 1

Factorize ..

${x}^{2} - x - 6$

Split the middle term

Such that their product will be -6

${x}^{2} - 3x + 2x - 6$

$x(x - 3) + 2(x - 3)$

$(x - 3)(x + 2)$

hope this helps ...

Answer 2

Solution:

Given equation:

$x {}^{2} - x - 6 = 0$

Let a = coefficient of x^2,b=coefficient of x and c= constant term

We would be using splitting the middle term method.

Now,

$ac = (1)( - 6) = - 6$

Splitting b in terms of factors of ac. i.e.,-6

•Factors of -6:

Six has four factors,one,two,three and the number itself(six).

We would be using 2 and -3

Now,

By splitting the middle term,

$x {}^{2} - x - 6 = 0 \\ \\ \\ \implies \: x {}^{2} - 3x + 2x - 6 = 0 \\ \\ \\ \implies \: x(x - 3) + 2(x - 3) = 0 \\ \\ \\ \implies \: (x - 3)(x + 2) = 0 \\ \\ \implies \: x - 3 = 0 \: \: or \: \: x + 2 = 0 \\ \\ \\ \implies \: \huge \boxed{x = 3 \: \: or \: \: - 2}$

The roots of given equation are 3 and -2