pls. factor x^3-7x+6
For factorizing the polynomial f(x) = x^3 - 7x + 6, we have to first find one value of x,
for which f(x) = 0 by hit and trial method.
For this we see the constant term + 6 and consider its factors ± 1, ± 2, ± 3, ± 6.
Putting these factors as the values of x, one by one in f(x), we find the value of x for which f(x) = 0.
That gives us the first factor of f(x). The rest we find either by continuing this process or by long division
by the factor that we have got.
On putting, x = 1 in f(x) = x^3 - 7x + 6, we get
f(i) = 1 – 7 + 6 = 0 => (x - 1) is a factor of x^3 - 7x + 6.
On putting, x = 2 in f(x), we get
f(2) = 8 – 14 + 6 = 0 => (x - 2) is a factor of x^3 - 7x + 6
On putting, x = -3 in f(x), we get
f( -3) = - 27 + 21 + 6 = 0
=>(x + 3) is a factor of x^3 - 7x + 6
Since the highest power of x in the expression is 3, there cannot be more than three factors.
Therefore, x^3 - 7x + 6 = (x - 1) (x - 2) (x + 3)