Question

+

The factors of x³ - 7x + 6 are :-
(A) x(x - 6) (x - 1)
(B) (x² - 6) (x - 1)
(C) (x + 1) (x + 2) (x - 3)
(D) (x - 1) (x + 3) (x - 2)​

Answer 1

Answer:

Let p(x)=x  

3

−7x+6

From figure, we have p(1)=0

Thus, (x−1) is a factor of p(x)

The other factor is x  

2

+x−6

=(x+3)(x−2)

Therefore, x  

3

−7x+6=(x−1)(x+3)(x−2)

Step-by-step explanation:

Answer 2

Answer:

Factors of x³-7x+6 are (x-1), (x+3) & (x-2)

Step-by-step explanation:

Put x = 1 :- (1)³-7(1)+6 = 0 therefore (x-1) is one the 3 factors of the equation.

To find the other 2 factors let's divide f(x) by (x-1) :

By dividing f(x) by (x-1) we'll get x²+x-6 as Quotient and 0 as remainder. Therefore, by mid-term splitting method :

x²+x-6 = (x+3)(x-2)

Since, Dividend = (Divisor x Quotient) + Remainder

=> x³ - 7x + 6 = (x-1)(x+3)(x-2)

Hence, we got all three factors of the given equation as ( x-1 ), ( x+3 ) and ( x-2 ).