Zeros of Polynomial Function

​Zeros of Polynomial Functions

By Salah kmali

Multiple Choice

Use synthetic division to completely factor: $$f\left(x\right)=x^3-6x^2+11x-6$$
use the given factor: (x-1)

• (x-1)(x-2)(x-3)

• (x-1)(x-2)(x-4)

• (x+1)(x+2)(x+3)

• (x-1)(x-2)(x+3)

Multiple Choice

What are the zeros of: $$f\left(x\right)=\left(x+1\right)\left(x^2-5x+6\right)$$

• [-1, 1, 3]
• [-1, -2, -3]

• [-1, 2, 3]
• [-2, 5, 6]

Multiple Choice

When using synthetic division, what are Coefficients for: $$f\left(x\right)=x^3+5x-1$$

• 1 5 -1

• 0 5 -1

• 1 0 5 -1

• 0 1 5 -1

Multiple Choice

Which of the following is a possible zero of: $$f\left(x\right)=2x^3+5x^2-x-6$$

• $$\frac{3}{2}$$

• $$\frac{5}{3}$$

• $$\frac{6}{5}$$

• $$\frac{7}{2}$$

Multiple Choice

Which of the following is not a possible zero of $$f\left(x\right)=3x^3-4x-2$$

• $$\frac{2}{3}$$

• $$\frac{-1}{3}$$

• $$-2$$

• $$\frac{4}{3}$$

Multiple Choice

Which of these is not a possible rational zero of: $$f\left(x\right)=3x^3-7x^2-22x+8$$

• $$\frac{1}{3}$$

• $$-\frac{8}{3}$$

• $$-\frac{4}{5}$$

• 4

Multiple Choice

Factor completely: $$f\left(x\right)=x^3-6x^2+11x-6$$

Find all the rational zeros.

• (x - 1)(x - 2)
• (x-1)(x-2)(x-3)

• (x+1)(x+2)(x+3)

• (x-1)(x-3)(x-4)