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Equations- Factorization of a polynomial equation – Exercise 5615

Exercise

Factor the polynomial equation

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

Final Answer


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

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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