factorization of x^3-3x+7 plz answer it step by step
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How do I factorize x^3 - 3x^2 + 3x + 7?
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since x=−1 satisfies the given cubic polynomial: x3−3x2+3x+7 hence (x+1) is a factor of x3−3x2+3x+7 Now factoring given cubic polynomial as follows
x3−3x3+3x+7=x2(x+1)−4x(x+1)+7(x+1)
=(x+1)(x2−4x+7)
Now, roots of x2−4x+7=0 are found by using quadratic formula as follows
x=−(−4)±(−4)2−4(1)(7)√2(1)=2±i3–√
Now, we factorize given quadratic polynomial: x2−4x+7 as follows
x2−4x+7=1(x−(2+i3–√))(x−(2−i3–√))=(x−2−i3–√)(x−2+i3–√)
Now, the real & complex factors of given cubic polynomial are as follows
x3−3x3+3x+7
=(x+1)(x2−4x+7)
=(x+1)(x−2−i3–√)(x−2+i3–√)
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