x^3- 3x^2-9x-5 Factories
Answers
Answer:
x³-3x²-9x-5
x³+x²-4x²-4x-5x-5
X²(X+1)-4x(x+1)-5(x+1)
(x+1)(x²-4x-5)
(x+1)[x²-5x+x-5]
(x+1)[x(x-5)+1(x-5)
(x+1)(x+1)(x-5)
(x+1)²(x-5)
Step-by-step explanation:
Spilit the Term of X²
Such that one of Number is of same cofficient as x³.And also keep in mind that another term of x² should be one of the sum or Difference in term of x.And remember the Constant term should (5) should be in sum or difference of term X
That will make it easier to Factorise.
Like Here.
x³-x²+4x²-4x-5x-5
Another Method
Firstly Find Factor of Constant term of given degree 3 Polynomial.
Like Here 5
5=±1,±5 is Factor.
Now
f(x)=x³-3x²-9x-5
Put value -1,+1,-5,+5 On place of X if you get Polynomial=0 then it will be root of Polynomial.
Step-by-step explanation:
Given Equation is x^3 - 3x^2 - 9x - 5
= > x^3 - 4x^2 + x^2 - 5x - 4x - 5
= > x^3 - 4x^2 - 5x + x^2 - 4x - 5
= > x(x - 4x - 5) + 1(x^2 - 4x - 5)
= > (x + 1)(x^2 - 4x - 5)
= > (x + 1)(x^2 + x - 5x - 5)
= > (x + 1)(x(x + 1) - 5(x + 1))
= > (x + 1)(x + 1)(x - 5)
= > (x + 1)^2(x - 5).
Hope this helps!