Question

(15 points please help)

solve each polynomial:
1. 15x^3-119x^2-10x+16=0
2. x^3-14x^2+47x-18=0
3. 5x^3-27x^2-17x-6=0

Answer 1

I find it useful to use a graphing calculator to find the zeros of higher-order polynomials. Once you find one or more rational zeros, you can factor them out to find the reduced polynomial factors (or you can use synthetic division).

1. This factors as (5x+2)(3x-1)(x-8). Roots are {-2/5, 1/3, 8}

2. This factors as (x-9)(x²-5x+2). Roots are {2.5-√4.25, 2.5+√4.25, 9}

3. This factors as (x-6)(5x²+3x+1). Roots are{-0.3-i√0.11, -0.3+i√0.11, 6}