X^3 -9x +2x^2 - 18 factor the polynomial
show your steps and tell what you did for each step

(x + 3)(x - 3)(x + 2) READ THE EXPLANATION I HAVE GIVEN PLEASE

Step-by-step explanation:

Let's just rearrange the expression to make it easier to factor...

  x³ - 9x + 2x² - 18 =

= x³ + 2x² - 9x - 18

Now, let's just factor the first two terms in the expression and the last two terms in the expression.

  x³ + 2x² - 9x - 18 =

= x² ( x  + 2 ) - 9 ( x + 2 )

= ( x² - 9 ) ( x + 2 )

We're not finished yet, we have to simplify the difference of squares. x² - 9 is the difference of squares because x² is a square and 3², also known as 9, is a square. x² - 9 is the difference of squares. The trick is with this simple algebraic expression:

a² - b² = (a + b)(a - b)

That means in the difference of squares, if you multiply the sum of the square root of each term and the difference of square roots of each term, they're equal. For this reason, x² - 9 = (x + 3)(x - 3). Test it out, it's still x² - 9!

  (x² - 9)(x + 2)=

= (x + 3)(x - 3)(x + 2)

That is the factorization of the polynomial.

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step-by-step explanation: