Question

Choose the factored form of the given equation. 6x 2 + 2x - 8 = 0

Answer 1

The factored form is : (3x + 4)(x - 1) = 0

Explanation:

The given quadratic equation is : 6x² + 2x - 8 = 0

To find the factored form :

6x² + 2x - 8 = 0

Take 2 common from the above equation

⇒ 2 × (3x² + x - 4) = 0

⇒ 3x² + x - 4 = 0

⇒ 3x² - 3x + 4x - 4 = 0

⇒ 3x(x - 1) + 4(x - 1) = 0

⇒ (3x + 4)(x - 1) = 0

`\implies\bf x =(-4)/(3)\textbf{ and }x = 1`

Answer 2

hello :

6x ² + 2x - 8 = 0
look when x= 1 : 6(1)²+2(1)-8 =6+2-8=0
6x²+2x-8 = (x-1)g(x)
g(x) = ax+b..... find : a and b
(x-1)(ax+b) =ax²+bx-ax-b =ax²+(b-a)x-b

ax²+(b-a)x-b = 6x ² + 2x - 8
a=6
b-a = 2
- b = -8
a=6 and b=8
6x²+2x-8 = (x-1)(6x+8)
(x-1)(6x+8) =0
x-1=0 or 6x+8=0
x=1 or x= -8/6= -4/3
the solutions are : 1 , -4/3