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.) (3)

Question

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.)

f(x) = 4x³ − 21x² + 35x − 18;    x − 1

Answer 1

By Factor Theorem f(x) divizible by (x - 1). We use synthetic division to get quotient:

1| 4 -21 35 -18

4 -17 18

4 -17 18 0

We have quotient and set equel 0 to get other zeros: 4x² - 17x + 18 = 0;

^{x = (17 ± √(289 - 288)/8; x = 9/4 or x = 2}

^{Solutions set: {1, 2, 9/4}}

Answer 2

If (x-1) is a factor then f(1) =0 which is true 4 -21+35-18=0

To find the remaining zeros divide the function by (x-1) which gives you 4x^2-17x+18. Factors this and you get

(x-2)(4x-9) =0 x=2 x=9/4