Roots of Polynomials

The degree of the polynomial determines the number of roots.

• True
• False

How many roots or zeros does the equation
f(x) = 5x⁴-8x³+4x²-6x+3 have?

• 3
• 4
• 5
• 0

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

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

The degree of a polynomial determines...

• the maximum number of x-intercepts

• the number of turning points

• if the end behavior is up or down

• the y-intercept

What is the factored form of the function shown?

• y = (x+3)(x-1)

• y = (x-3)(x-1)

• y = (x+3)(x+1)

• y = (x-3)(x+1)

Find all rational zeros, one zero has been given.
f(x) = x³-5x²-2x+24;   -2

• -2,1,0
• -2,-3,-4
• 4,3,-2
• 0,0,0

• When the remainder is 0 using synthetic division.

• When the remainder is 0 using long division.

List the potential real zeros of:
f(x) = 5x³ - x² + 3

• ±1/5, ±3/5, ±1, ±3
• ±1/3, ±5/3, ±1, ±5
• ±1/5, ±3/5, ±1, ±3, ±5
• ±1/5, ±1/3, ±1, ±3, ±5

True or False: If (7x + 4) is a factor of some polynomial function, then 4/7 is a zero of the function.

Which of these is a possible root of the polynomials?
x³ - 6x² - x + 30

• 0
• 4
• -9
• -15