Question

Thevolumeincubicfeetofaboxcanbeexpressedas (푥)=푥ﰆ −6푥ﰇ +8푥,or as the product of three linear factors with integer coefficients. The width of the box is 2 – x.
Factor the polynomial to find linear expressions for the height and the width.

Answer 1

\[(x)=x^3-6x^2+8x\]

Answer 2

well start by looking at

\[f(x) = x(x^2 -6x + 8)\]

so i linear factor is x

factor the quadratic in brackets to find the other linear factors.

Answer 3

let me be honest , ihave no clue ive been learing off the internet but im completly lost w/ this

Answer 4

ok... so look for 2 numbers that multiply to 8 and add to -6, they are both negative.

Answer 5

well you know the width 2 - x

and there is a factor of x so the 3rd factor is (4 - x)

so your volume is f(x) = x(2-x)(4 -x)

so if width is (2 - x)
height is x
length is (4 - x)

Answer 6

ook im getting it thank you!

Answer 7

how do i put in linear expression @campbell_st ?

Answer 8

tahts weird i used to live on campbell st in chicago

Answer 9

the linear expressions are just x, 2 -x and 4 -x

linear just means the highest power is 1

lol... well thats weird... I lived on a campbell_st in Australia.

Answer 10

and an expression is just an arrangement of letters and numbers.

if you include an equals sign, you get an equation.

Answer 11

ugh for some reason im really slow on this and not putting in right equation

Answer 12

well the 3 things multiplied given the volume

V = length x width x height

the 3 linear expressions you have are

length = x width = 2 -x so height = 4 - x

length and height are interchangable.

Answer 13

oh wow gotcha ... #embarrasing