Answer:
The zeros are -1/2, 1/3 and 2.
The factors are (x - 2)(3x - 1)(2x + 1)
Step-by-step explanation:
h(x)= 6x^3 - 11x² - 3x + 2 = 0
As the last term is 2 we try to see if +/-1 or +/- 2 are zeros
f(1) = -6, f(-1) = -18 so they are not zeros.
f(2) = 6*8 - 11*4 - 3(2) + 2
= 48 - 44 - 6 + 2
= 4 - 6 + 2
= 0.
So x = 2 is a zero and x - 2 is a factor.
Dividing by x - 2:
x - 2 ) 6x^3 - 11x² - 3x + 2 ( 6x^2 + x - 1 <--------Quotient
6x^3 - 12x^2
x^2 - 3x
x^2 - 2x
- x+ 2
-x + 2
Factoring the quotient:
6x^2 + x - 1
= (3x - 1)(2x + 1) = 0
x = 1/3, x = -1/2..
