Question

16. Factorise : x3-15x2+74x-120.​

Answer 1

Concept :

Variables and coefficients make up polynomials, which are algebraic expressions. Indeterminates are another term for variables. For polynomial expressions, we can do mathematical operations such as addition, subtraction, multiplication, and positive integer exponents, but not division by variable.

Given :

$x^{3}-15 x^{2}+74 x-120$

Find :

Factorize the given equation

Solution :

$x^{3}-15 x^{2}+74 x-120$

$=(x-4) \frac{x^{3}-15 x^{2}+74 x-120}{x-4}\\\frac{x^{3}-15 x^{2}+74 x-120}{x-4}=x^{2}-11 x+30\\=(x-4)(x^{2}-11 x+30)\\=(x-4)(x-5)(x-6)$

Answer 2

Factorize :-

x³ -15x² + 74x -120

⇒ x³ -9x² -6x² + 20x + 54x -120

⇒( x³ -9x² + 20x ) ( 6x² + 54x - 120 )

⇒  x ( x² - 9x + 20) - 6 ( x² -9x + 20 )

⇒ ( x-6) ( x² -9x +20)

⇒( x - 6 ) ( x² - 5x - 4x + 20 )

⇒ ( x - 6 ) [ x ( x -5 ) - 4 ( x - 5 ) ]

⇒( x - 6 ) ( x - 4 ) ( x - 5 )

Ans :- ( x - 6 ) ( x - 4 ) ( x - 5 )