Is (x + 2) a factor of
x^3 - 4x^2 + 2x - 3?

-2x3-4x2-6x

Final result :

-2x • (x2 + 2x + 3)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

((0 -  (2 • (x3))) -  22x2) -  6x

Step  2  :

Equation at the end of step  2  :

((0 -  2x3) -  22x2) -  6x

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

 -2x3 - 4x2 - 6x  =   -2x • (x2 + 2x + 3)

Trying to factor by splitting the middle term

4.2     Factoring  x2 + 2x + 3

The first term is,  x2  its coefficient is  1 .

The middle term is,  +2x  its coefficient is  2 .

The last term, "the constant", is  +3

Step-1 : Multiply the coefficient of the first term by the constant   1 • 3 = 3

Step-2 : Find two factors of  3  whose sum equals the coefficient of the middle term, which is   2 .

    -3    +    -1    =    -4

    -1    +    -3    =    -4

    1    +    3    =    4

    3    +    1    =    4

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

-2x • (x2 + 2x + 3)

Step-by-step explanation:

65/16 exact form, 4.0625 in decimal form, and 4 1/16 in mixed number form.