When Mai rewrites x² + 5 · x = 0 as x · (x + 5) = 0, she can find two values of x such that the equation is solved, that is, the second order polynomial becomes zero.
How to find the roots of a polynomial by factoring a second order polynomial
Factoring the polynomial is derived from the algebraic theorem that states that if x · y = 0, then x = 0 or y = 0. In addition, the polynomial is factored form consists in the following product of binomials:
[tex]\prod \limits_{i=1}^{n} (x-r_{i})=0[/tex] (1)
Where [tex]r_{i}[/tex] is the i-th root of the polynomial.
Hence, when Mai rewrites x² + 5 · x = 0 as x · (x + 5) = 0, she can find two values of x such that the equation is solved, that is, the second order polynomial becomes zero.
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