Math, asked by oscarpaul6767, 10 months ago

Factorise: (i) x 3 − 2x 2 − x + 2 (ii) x 3 + 3x 2 −9x − 5 (iii) x 3 + 13x 2 + 32x + 20 (iv) 2y 3 + y 2 − 2y − 1

Answers

Answered by kokeyking
3

Answer:

Step-by-step explanation:

x3-2x2-x+2  

Final result :

 (x + 1) • (x - 1) • (x - 2)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (((x3) -  2x2) -  x) +  2

Step  2  :

Checking for a perfect cube :

2.1    x3-2x2-x+2  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  x3-2x2-x+2  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -x+2  

Group 2:  x3-2x2  

Pull out from each group separately :

Group 1:   (-x+2) • (1) = (x-2) • (-1)

Group 2:   (x-2) • (x2)

              -------------------

Add up the two groups :

              (x-2)  •  (x2-1)  

Which is the desired factorization

Trying to factor as a Difference of Squares :

2.3      Factoring:  x2-1  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check :  x2  is the square of  x1  

Factorization is :       (x + 1)  •  (x - 1)  

Final result :

 (x + 1) • (x - 1) • (x - 2)

Similar questions