Thread: Algebra polynomial

I'm having problems solving this one. Please help

The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3 + i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.

choices
f(x) = (x+4)(x^2+6x+10)
f(x) = (x-4)(x^2-6x-9
f(x) = (x-4)x^2-6x+10)
f(x) = (x-4)(x^2-6x+9)

Originally Posted by wvmcanelly@cableone.net

I'm having problems solving this one. Please help

The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3 + i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.

All such non-zero polynomials difference by a constant multiple. So we will find one which has 1 as its leading coefficient (called monic).

Now if f(x) is a polynomial in R[x] (meaning the real numbers) and if a+bi is a zero then a-bi is also a zero.
So if 3+i is a zero that means 3-i is a zero.

Thus,

Multiply the last two factors together,

thanks, good not have figured that one out without you.