factorise the polynomial x³ - 6x² 3x 10 .given that the factor is (X 1)​?

VTPETERS2002

5 years ago

Let f(x) = x3 – 6x2 + 3x + 10
Constant term = 10
Factors of 10 are ±1, ±2, ±5, ±10
Let x + 1 = 0 or x = -1
f(-1) = (-1)3 – 6(-1)2 + 3(-1) + 10 = 10 – 10 = 0
f(-1) = 0

Let x + 2 = 0 or x = -2
f(-2) = (-2)3 – 6(-2)2 + 3(-2) + 10
= -8 – 24 – 6 + 10 = -28
f(-2) ≠ 0

Let x – 2 = 0 or x = 2
f(2) = (2)3 – 6(2)2 + 3(2) + 10
= 8 – 24 + 6 + 10 = 0

f(2) = 0 Let x – 5 = 0 or x = 5

f(5) = (5)3 – 6(5)2 + 3(5) + 10
= 125 – 150 + 15 + 10 = 0
f(5) = 0

Therefore, (x + 1), (x – 2) and (x - 5) are factors of f(x)

Hence f(x) = (x + 1) (x – 2) (x - 5)