# Equations- Factorization of a polynomial equation – Exercise 5613

Exercise

Factor the polynomial equation

$$2x^3+5x^2-2x-5=0$$

$$(2x+5)(x-1)(x+1)=0$$

Solution

$$2x^3+5x^2-2x-5=$$

We extract a common factor from the first two expressions:

$$=x^2(2x+5)-2x-5=$$

We arrange the last two expressions to be exctly as the expression in parentheses:

$$=x^2(2x+5)-(2x+5)=$$

Once again we extract a common factor – this time the expression in parentheses:

$$=(2x+5)(x^2-1)=$$

We break down the second factor using Short Multiplication Formulas (third formula) and get the factorizing:

$$=(2x+5)(x-1)(x+1)$$

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