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Solve the polynomial equation by factoring and then using the zero product principle

Solve the polynomial equation by factoring and then using the zero product principle-example-1
User Kamalanathan
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1 Answer

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14 votes

Given;


x^3+2x^2=16x+32

To find: The equation in factored form and solution set.

Step-by-step explanation:

Given equation can be written as


x^3+2x^2-16x-32=0
\begin{gathered} \text{When x=-2, The equation becomes,} \\ -8+8+32-32=0 \\ 0=0 \\ \text{Then (x+2) is a factor of given equation.} \end{gathered}

By using the factor (x+2), We proceed with the synthetic division


\begin{gathered} x^3+2x^2-16x-32=0 \\ (x+2)(x^2-16)=0 \\ (x+2)(x^2-4^2)=0 \\ (x+2)(x+4)(x-4)=0 \end{gathered}

Therefore, the equation is factored form:


(x+2)(x+4)(x-4)=0

Then the solution set is


\mleft\lbrace-2,-4,4\mright\rbrace

Solve the polynomial equation by factoring and then using the zero product principle-example-1
User Ahmkara
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