Find all roots

State 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

Write a polynomial function of least degree in standard form that has the following roots: 
 $-3,\ \sqrt{5}$  

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

•  $f\left(x\right)=\left(x-3\right)\left(x-\sqrt{5}\right)$  

•  $f\left(x\right)=x^3+3x^2-5x-15$  

•  $f\left(x\right)=x^3-3x^2+5x+15$  

is -3 a zero of $f\left(x\right)=3x^3+2x^2-5x+2$ ? 

• yes

• no

Is (x - 2) a factor of f(x)= x³ - 8x² + 14x - 4?

• Yes, (x - 2) is a factor. There is a remainder.

• No, (x - 2) is not a factor. The remainder is zero.

• Yes, (x - 2) is a factor. The remainder is zero.

• No, (x - 2) is not a factor. There is a remainder.

Find all rational zeros, one zero has been given.

f(x) = x³ - 3x² - x + 3; 3

• 2, 4, 3

• -1, 1, 3

• 3, 2, 1

• 4, 5, 6

State 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

State all zeros of the polynomial 4x³ - 17x² - 150x - 189 if one zero is 9.

• -3, -9, 0

• -7, 9, -3

• -3, -7/4, 9

• -3, -4/7, 9

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

Find all zeroes given a factor of (x + 3).

f(x) = 2x³ + 5x² - 6x - 9

• -1, -3, -3

• -1, -3, 3/2

• 3, 3, 3

• -3, 2/3, -1

Is (x - 3) a factor of (x³ - 3x² + 2x + 2)?

• Yes

• No