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. [tex]6x^{3} +7x^{2} -1;(2X+1)[/tex]
Accepted Solution
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Answer:The factors are (2x + 1) , (3x - 1) and (x + 1)The zeroes are -1/2 , 1/3 , -1Step-by-step explanation:(6x³ + 7x² + 0 - 1) ÷ (2x + 1) =3x² + (4x² + 0 - 1) ÷ (2x + 1) =3x² + 2x + (-2x - 1) ÷ (2x + 1) =3x² + 2x - 1By using factorization3x² + 2x - 1 = (3x - 1)(x + 1)The factors are (2x + 1) , (3x - 1) and (x + 1)To find the zeroes2x + 1 = 0 ⇒ 2x = -1 ⇒ x = -1/23x - 1 = 0 ⇒ 3x = 1 ⇒ x = 1/3x + 1 = 0 ⇒ x = -1The zeroes of the polynomial are -1/2 , 1/3 , -1