Please Help! Step by Step please 1.) A polynomial f(x) with real coefficients an
ID: 3096304 • Letter: P
Question
Please Help! Step by Step please1.) A polynomial f(x) with real coefficients and leadingcoefficient 1 has zeros 9, -1 - 6i and degree 3. Express f(x) as aproduct of linear and quadratic polynomials with real coefficientsthat are irreducible over R.
2.) A polynomial f(x) with real coefficients and leadingcoefficient 1 has zeros 3 + 8i, -8 + i and degree 4. Express f(x)as a product of quadratic polynomials with real coefficients thatare irreducible over R.
3.) A polynomial f(x) with real coefficients and leadingcoefficient 1 has zeros 0, -6i, 8 i and degree 5. Expressf(x) as a product of linear and quadratic polynomials with realcoefficients that are irreducible over .
4.) A polynomial f(x) with real coefficients and leadingcoefficient 1 has zeros -5, 0, 6 + i and degree 4. Express f(x) asa product of linear and quadratic polynomials with realcoefficients that are irreducible over R.
Explanation / Answer
1.) f(x)=(x-9)(x+1+6i)(x+1-6i) =(x-9)(x^2+2x+37) 2.) f(x)=(x-3-8i)(x-3+8i)(x+8-i)(x+8+i) =(x2_6x+73)(x^2-16x+65)3.) f(x)=x(x+6i)(x-6i)(x-8+i)(x-8-i)
=x(x^2+36)(x^2-16x+65)
4.)f(x)=x(x+5)(x-6-i)(x-6+i)
= x(x+5)(x^2-12x+37)
6x+73