Question

Factorise
${x}^{2} - 6x - 7$
using factor theorem​

Answer 1

(+ I edited the incorrect part)

$x^2-6x-7$ will be factorised into (x-α)·(x-β)

By rational root theorem

Possible values of α and β are ±1, ±7

x=1

1-6-7≠0

x=-1

1+6-7=0

x=7

49-42-7=0

x=-7

49+42-7≠0

Two zeros are -1 and 7.

By factor theorem, two factors are x+1, x-7

$x^2+6x-7=(x+1)(x-7)$

Answer 2

Given equation

$x^{2} -6x-7=0$

Solving, we get,

$x^{2} -6x-7=0$

$\implies x^{2} -7x+x-7=0$

$\implies x(x-7)+1(x-7)=0$

$\implies (x+1)(x-7)=0$

Now,

$x+1=0\\\implies x = -1$

$x-7=0\\\implies x = 7$

$\boxed{\boxed{\bold{Therefore, \ the \ factorised \ expression \ is \ (x+1)(x-7)}}}}}}}}}$