Find all the factors of x^3+2x^2-x-2 please help
Answers
Answer:
A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation.
A polynomial can be written as the product of its factors having a degree less than or equal to the original polynomial.
The process of factoring is called factorization of polynomials.
Given that x3 – 2x2 – x + 2
Grouping the 1st and 3nd terms together and the 2nd and 4th term together:
= x(x2 – 1) – 2(x2 – 1)
x3 – 2x2 – x + 2 = (x2 – 1) (x – 2)
Using the identity: a2 − b2 = (a + b) (a- b)
∴ (x2 – 1) = (x + 1)(x – 1)
= (x – 1) (x + 1) (x- 2)
∴ answer is (x – 1) (x + 1) (x- 2)
Step-by-step explanation:
Given :-
x³+2x²-x-2
To find :-
Find all the factors ?
Solution :-
Given expression is x³+2x²-x-2
It can be written as
=> (x³+2x²)-(x+2)
=> x²(x+2)-1(x+2)
=> (x+2)(x²-1)
=> (x+2)(x²-1²)
We know that
(a+b)(a-b) = a²-b²
Where, a = x and b = 1
=> (x+2)(x+1)(x-1)
Therefore,
x³+2x²-x-2 = (x+2)(x+1)(x-1)
Answer:-
The factors of the given expresion are (x-1) , (x+1) and (x+2)
Used formulae:-
- (a+b)(a-b) = a²-b²