Question

factorization of x^3-3x+7 plz answer it step by step​

Answer 1

Answer:

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–√)