Question

Use Synthetic Division to Factor the following polynomials completely by given factors or roots and Find all the zeros; When you reach quadratic equation, performance regular factoring or Quadratic Formula.


`6x^(3) +7x^(2) -1;(2X+1)`

Answer 1

The factors are (2x + 1) , (3x - 1) and (x + 1)

The zeroes are -1/2 , 1/3 , -1

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