Solving Polynomials

Find all the real zeros of the function 
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

• x = 1/2, -6

• x = -1/2, 6

• x = 4, -1/2, 6

• x = -4, 1/2, -6

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

• x-intercept

• zero

• root

• all of these.

Factor:
x² - 400

• ( x - 200) ( x + 200) 

• ( x + 20) ( x + 20) 

• Prime

• ( x - 20) ( x + 20) 

Is the binomial x - 9 a factor of 4x² -33x -27?

• yes

• no

x³-3x²-10x+24 ÷ x+3 (Use synthetic division.)

• x²-7x+5

• x-8

• x²-6x+8

• x+9

Let f(x) = 3x² - 9x +2.
Is k = -3 a zero of the function? (Prove by using synthetic division.

• yes

• no

Factor:
 f(x) = x³-12x²+47x-60=0 when 5 is a zero. (so f(5) = 0)

• (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

What is the remainder when the polynomial p(x) is divided by (x-5)?
p(x) = x³ - 5x² + 2x - 10

• 0

• -10

• -2x-10

• 2

What is the proper way to write the answer for the following problem? 

• 2x³-x²-25x-12

• 2x⁴-x³-25x²-12x+0

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

• -1,-3,-3

• -1,-3,3/2

• 3,3,3

• -3,2/3,-1