Question

If (x – 2) is a factor of x³ – mx² + 10x – 20, then find the value of m.

Answer 1

p(x) = x³ – mx² + 10x – 20 x – 2 is a factor of x³ – mx² + 0x – 20. 

∴By factor theorem, 

Remainder = p(2) = 0 

p(x) = x³ – mx² + 10x – 20 

∴ p(2) = (2)³ – m(2)² + 10(2) – 20 

∴ 0 = 8 – 4m + 20 – 20 

∴ 0 = 8 – 4m 

∴ 4m = 8 

∴ m = 2