Question

Factor the polynomial as the product of three binomials.
Note: Try using factor theorem for guessing some of the
factors.
x^3 - 4x^2 + 5x - 2 =​

Answer 1

Answer:

f(x) = X^3- 4X^2 + 5X -2

factors of -2 are -1,+1

let (x-1) and (x-2) are the factors of x^3-4x^2+5x-2

now putting x-1=0

f (1 ) = (1)^3-4(1)^2+5(1)-2

= 1 -4+5-2

= 0

yes (x-1) is the factor of f(x)

To find other factors we have to divide f(x) by (x-1)

(X^3-4X^2+5X-3)/(x-1) = X^2-3X+2

f(x) = (x-1) ( X^2-3X+2)

= (X-1) (X^2-2x-1x+2)

= (X-1) [x(x-2)-1(x-2)]

= (x-1)(x-1)(x-2)