Answer:
The factors are (2x + 1) , (3x - 1) and (x + 1)
The zeroes are -1/2 , 1/3 , -1
Step-by-step explanation:
(6x³ + 7x² + 0 - 1) ÷ (2x + 1) =
3x² + (4x² + 0 - 1) ÷ (2x + 1) =
3x² + 2x + (-2x - 1) ÷ (2x + 1) =
3x² + 2x - 1
By using factorization
3x² + 2x - 1 = (3x - 1)(x + 1)
The factors are (2x + 1) , (3x - 1) and (x + 1)
To find the zeroes
2x + 1 = 0 ⇒ 2x = -1 ⇒ x = -1/2
3x - 1 = 0 ⇒ 3x = 1 ⇒ x = 1/3
x + 1 = 0 ⇒ x = -1
The zeroes of the polynomial are -1/2 , 1/3 , -1
