Equations- Factorization of a polynomial equation – Exercise 5615

Exercise

Factor the polynomial equation

$x^3+5x^2-4x=20$

Final Answer

Show final answer

Solution

$x^3+5x^2-4x=20$

We move everything to one side of the equation:

$x^3+5x^2-4x-20=0$

We extract a common factor from the first two expressions:

$x^3+5x^2-4x-20=$

$=x^2(x+5)-4x-20=$

We also extract a common factor from the last two expressions:

$=x^2(x+5)-4(x+5)=$

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

$=(x+5)(x^2-4)=$

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

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

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