Roots and Zeros of Polynomials

Find all zeros:
ƒ(x) = x(2x + 1)(x - 2)

• x = 0, -½, 2
• x = 0, ½, 2
• x = 0, -½, -2
• x = 0, -2, 2

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

• x = -4, x = 3, x = -2
• x = -4, x = 3, x = 2 
• x = -4, x = -3, x = 2
• x = 4, x = 3, x = 2

Identify the real zeros

• x=2, x=6, x=-4

• (x+2)(x+6)(x-4)

• (x-2)(x-6)(x+4)

• x=-2, x=-6, x=4

Write a polynomial in factored form with zeros at x = 1, x = -1 x = 0

• (x - 1)(x + 1)

• x(x - 1)(x + 1)

• x²(x - 1)(x + 1)

• x(x - 1)(x - 1)

f(x) = 2x³ - 3x² + 4x -10

What is the degree of f(x)?

• 3

• 2

• 1

• 0

Find all zeros. One zero has been given.
f(x) = x⁴ + 8x³ + 14x² - 8x - 15; x = -5

• -2,1,-1,-5
• -3,1,-1,-5
• 3,-3,4,0
• -1,1-5,3

Factor f(x)= x³ - 2x²-13x - 10  given that (x - 5) is one factor.

• (x- 5)(x - 1)(x - 2)
• (x - 5)(x + 2)(x - 2)
• (x - 5)(x + 2) (x + 1)
• (x - 5)(2x - 13)

Factor:
 x³-12x²+47x-60=0 when 5 is a root.

• (x-3)(x-4)(x-5)=0
• (x+1)(x-4)(x-5)=0
• (x-3)(x-4)(2x-5)=0
• (x-5)(x-4)(x-5)=0

The degree of the polynomial determines the number of roots.

• True
• False

What is another way to say "where a function crosses the x-axis"?

• x-intercept
• zero
• root
• all of these.