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step 1:explanation: to solve the equation −3z3+140−139z+38z2=0 to solve the equation −3z3+140−139z+38z2=0 using synthetic division and the factor theorem, first, we need to find the potential roots of the equation. the possible rational roots are factors of the constant term (140) divided by factors of the leading coefficient (-3). potential roots include ±1, ±2, ±4, ±5, ±7, ±10, ±14, ±20, ±28, ±35, ±70, and ±140.step 2:explanation: now, perform synthetic division to test each potential root to see if it's a solution. start with the root -1: -3 | 1 38 -139 140 -3 -35 174 ----------------------- 1 35 -174 314 the remainder is 314, which is not zero. continue testing other potential roots until you find one that yields a remainder of 0. when you find such a root (let's say it's z=k), then (z−k) is a factor of the polynomial. you can then use synthetic division again to find the other factor.step3:explanation:

the expansion of the logarithmic expression \ln(x^{-4}x^{4}y^2} simplifies to: \ln(x^{-4}x^{4}y^2}) = \ln(1) = 0

a) expression to represent flow's staff tenure: let g represent the number of years gio has worked. then, nakita has worked g+8 years, and kevisha has worked g+(g+8)−3 years. the expression for flow's staff tenure is: flow=g+(g+8)+(g+(g+8)−3)=4g+13 b) expression to represent digicel staff tenure: nyra's tenure from digicel is the same as nakita's, which is g+8, and danaldo has worked 20 years. the expression for digicel's staff tenure is: digicel=g+8+20=g+28step 4: explanation: c) inequality to represent the information: c) inequality to represent the information: since the problem states that digicel staff's tenure is greater than flow's staff, we can write the inequality as: digicel>flow substitute the expressions from parts (a) and (b) into the inequality: g+28>4g+13 now, solve for g: 15>3g 5>g so, the tenure of gio (g) must be less than 5 years for digicel staff's tenure to be greater than flow's staff.final answer:1. to solve the equation −3z^3+140−139z+38z^2=0, you would use synthetic division and the factor theorem to find the roots (solutions) of the equation. 2. the expansion of the logarithmic expression invalid math simplifies to 0. 3. a) flow's staff tenure can be represented as flow=4g+13. b) digicel's staff tenure can be represented as digcel=g+28. c) the inequality representing the information is 5>g, which means gio's tenure must be less than 5 years for digicel's staff tenure to be greater than flow's staff.

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