If x+ 2 and x – 1 are the factors of x³ + 10x² + mx + n, the find the value of m and n.

Concept Used:

Factor theorem: If (x – a) is a factor of f(x), then f(a) = 0

Explanation:

Let f (x) = x³+10x² +mx + n

Since, (x + 2) and (x – 1) are factor of f (x)

So, f (–2) = 0

(–2)³ + 10 (–2)² + m (–2) + n

32 – 2m + n = 0 (i)

f (1) = 0

(1)³ + 10 (1)² + m (1) + n = 0

11 + m + n = 0 (ii)

(2) – (1)

3m –21 = 0

m = 7 (iii)

Using (iii) and (ii), we get

11 + 7 + n= 0

n = – 18