If (x – 1) divides mx³ – 2x² + 25x – 26 without remainder find the value of m

mx³ – 2x² + 25x – 26 is divided by (x – 1) without remainder that means remainder = 0

Remainder theorem states that if p(x) is any polynomial and a is any real number and If p(x) is divided by the linear polynomial (x – a) , then the remainder is p(a).

Let p(x) mx³ – 2x² + 25x – 26 and we have (x – 1)

The zero of (x – 1) is 1

Now using Remainder theorem,

p(x) = mx³ – 2x² + 25x – 26 is divided by x – 1 then, p(1) is the remainder which is 0

p(1) = mx³ – 2x² + 25x – 26 = 0

= m(1)³ – 2(1)² + 25(1) – 26 = 0

= m – 2 + 25 – 26 = 0

= m – 3 = 0

m = 3