9514 1404 393
Answer:
a) zeros: -2/3, 6
b) x < -2/3, signs: -, -; sign of product: +
-2/3 < x < 6, signs: +, -; sign of product: -
x > 6, signs: + +; sign of product: +
c) solution: x < -2/3 ∪ x > 6
Explanation:
a) The zeros of the product are the values of x that make either factor zero. (A product is only zero if one of the factors is zero.)
3x +2 = 0 ⇒ x = -2/3
x -6 = 0 ⇒ x = 6
The zeros of the quadratic are x = -2/3 and x = 6.
__
b) For values of x left of the left-most zero, both factors are negative. For values of x between the zeros, the left factor is positive and the right factor is negative. For values of x greater than the right-most zero, both factors are positive. That is, for large negative values of x, all factors are negative. Working left-to-right, each time a zero is crossed, one factor changes sign.
__
c) The solution is where the signs of the factors match:
x < -2/3 or -6 < x