Using Remainder Theorem, factorise :

x³ + 10x² - 37x + 26 completely.

For x = 1, value of x³ + 10x² - 37x + 26,

= (1)³ + 10(1)² - 37(1) + 26

= 1 + 10 - 37 + 26

= 37 - 37

= 0.

Hence, (x - 1) is factor of x³ + 10x² - 37x + 26.

On dividing, x³ + 10x² - 37x + 26 by (x - 1),

$\begin{array}{l} \phantom{x - 1)}{x^2 + 11x - 26} \ x - 1\overline{\smash{\big)}x^3 + 10x^2 - 37x + 26} \ \phantom{x - 1}\underline{\underset{-}{}x^3 \underset{+}{-}x^2} \ \phantom{{x - 1}2x^3+4}11x^2 - 37x \ \phantom{{x - 1}2x^3+}\underline{\underset{-}{}11x^2 \underset{+}{-} 11x} \ \phantom{{x - 1}{2x^3+}{+11x^2}}-26x + 26 \ \phantom{{x - 1}{2x^3+}{+11x^2}}\underline{\underset{+}{-}26x \underset{-}{+} 26} \ \phantom{{x - 1}{2x^3+}{+2x^2-}{-4x}}\times \end{array}$

we get, quotient = x² + 11x - 26.

Factorising x² + 11x - 26,

= x² + 13x - 2x - 26

= x(x + 13) - 2(x + 13)

= (x - 2)(x + 13).

Hence, x³ + 10x² - 37x + 26 = (x - 1)(x - 2)(x + 13).