A polynomial P is given. P(x)=x3−2x2+9x−18 a) Factor P into linear and irreducible quadratic factor with real coefficients. P(x)=? b) Factor P completely into linear factors with complex coefficients. P(x)=?

Question

A polynomial P is given.  P(x)=x3−2x2+9x−18  a) Factor P into linear and irreducible quadratic factor with real coefficients.  P(x)=?  b) Factor P completely into linear factors with complex coefficients.  P(x)=?

Jaylen Fountain · Accepted Answer

p(x)=x3−2x2+9x−18  a) =x2(x−2)+9(x−2)  =(x−2)(x2+9)  Hence p(x)=(x−2)(x2+9)  where (x−2) is linear (x2+9) is irreducible quadratic factors.  b) p(x)=(x−2)(x2+9)  =(x−2)(x2+32)  =(x−2)(x2−i232)(asi2=−1)  =(x−2)(x2−(3i)2)  p(x)=(x−2)(x−3i)(x+3i)  Three linear factors are:  (x−2)(x−3i) and (x+3i)  where (x−3i) and (x+3i) have complex coefficients.

A polynomial P is given. P(x)=x^{3}-2x^{2}+9x-18 a) Factor P into linear and

Answered question

Answer & Explanation

New Questions in Pre-Algebra