Understanding zeroes and factors of polynomials

 $If\ \alpha\ and\ \beta\ are\ zeroes\ of\ f\left(x\right)=px^2-2x+3p\ \ \ and\ \ \ \ \ \alpha+\beta=\alpha\beta\ \ \ \ then\ find\ p$  

(a)  

Write in factored form using the following roots.

7, -2i

• (x-7)(x-2i)

• (x-7)(x+2i)(x-2i)

• (x-7)(x+2i)

• (x-7)(x+7)(x-2i)

Write a polynomial function of least degree with integral coefficients and have zeros 2, 1, -1.

• x³ - 2x² - x + 2

• x³ + 2x² - x + 2

• x³ - 2x² - x - 2

• x³ - 2x² + x + 2

• -4

• -3

• -2

• 2

• 4

Which polynomial function represents this graph?

• f(x) = (x + 7)(x + 5)(x – 5)

• f(x) = (x + 7)(x – 5)(x + 5)

• f(x) = (x + 7)(x + 5)(x + 5)

• f(x) = (x – 7)(x – 5)(x – 5)

Select a polynomial function of degree 6 whose zeros are given.

Zeros: – 4(multiplicity of 2), 5(multiplicity of 2), – 1, 6

•  $f\left(x\right)=(x+4)^4(x-5)^2(x+1)(x-6)$ 
  

•  $f\left(x\right)=(x+4)^2(x-5)^2(x+1)^{ }(x-6)^{ }$ 
  

•  $f\left(x\right)=(x+4)^3(x-5)^2(x+1)$ 
  

•  $f\left(x\right)=(x+4)^2(x-5)(x+1)(x-6)$ 
  

Write the factored form of the graph.

• y=x(x-2)(x-4)(x-1)

• f(x)=(x+2)(x-1)(x-4)

• g(x)=(x+1)(x+2)(x-1)(x-4)

• h(x)=x(x+2)(x-1)(x-4)

• A

• B

• C

• D

Which equation matches a graph with x-intercepts x=5 and x= -7 ?

• (x+5)(x-7)=0

• (x-5)(x+7)=0

• (x+5)(x+7)=0

• (x-5)(x-7)=0

Which of the following could be the factored form for the equation representing the graph shown?

• (x+3)(x-2)(x-5)
• (x-5)²(x-2)(x+3)
• (x-3)(x+2)(x+5)²
• none of these