Given that x+2 and 3x-1 are factors of the expression 3x^3-10x^2+px+q, find the values of p and q. Hence find the third factor of the expression.

Step-by-step explanation:

x + 2 = 0

x = -2

3x - 1 = 0

x = ⅓

Substitution :

3x³ - 10x² + px + q = 0

3(-2)³ - 10(-2)² + p(-2) + q = 0

-24 - 40 - 2p + q = 0

-2p + q = 64… Equation 1

3x³ - 10x² + px + q = 0

3(1/3)³ - 10(1/3)² + p(1/3) + q = 0

1/9 - 10/9 + ⅓ p + q = 0

- 1 + ⅓ p + q = 0

⅓ p + q = 1

p + 3q = 3… Equation 2

Elimination Equation 1 and 2 (times 2) :

-2p + q = 64

2p + 6q = 6

___________ +

7q = 70

q = 10

find p subtitution value of q to equation :

example from second Equation…

p + 3q = 3

p + 3(10) = 3

p + 30 = 3

p = 3 - 30

p = -27

∴ So, value of p = -27, q = 10, and the third factor is (3x - 15)

this answer is !

17.08

correct me if i am wrong.