Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)

Question

f(x) = 8x³ − 33x² + 43x − 18;    x − 1

Answer 1

8x^3 -33x^2 +43x -18

by DesCartes rule there are 3 possible positive zeros

and zero possible negative zeros

there's at least one positive zero or at most 3, but not two, as that would leave 1 imaginary zero, and imaginary zeros come in conjugate pairs

18/8, 18/4, 18/2, 18/1, 9/8, 9/4, 9/2, 9/1, 6/8, 6/4, 6/2, 6/1, 3/8, 3/4, 3/2, 3/1, 1/8, 1/4, 1/2, 1/1, are the possibilities

ignore negative possibilities

try simple integers first such as 1, 3, 6, 9, 18

try 1 first, it works, 1 is a zero

x-1 is a factor

divide the cubic by x-1, by long or synthetic division

to get a quadratic

8x^2 -25x +18

factor

=(x-2)(8x-9)

8x^3-33x^2+43-18 = (x-1)(x-2)(x-9/8)

zero are 1,9/8, 2

or 1, 1.125, 2

or try a math calculator on line, such as Mathpapa.com. It factors for you