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OpenStudy (anonymous):
yes
OpenStudy (anonymous):
The volume in cubic feet of a box can be expressed as V(x) = x^3 - 6x^2 + 8x, 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. Show steps please
OpenStudy (anonymous):
@jim_thompson5910
jimthompson5910 (jim_thompson5910):
x^3 - 6x^2 + 8x
x(x^2-6x+8)
x(2-x)( ??? )
jimthompson5910 (jim_thompson5910):
what goes in place of the ( ??? )
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OpenStudy (anonymous):
@jim_thompson5910 -6x + 8?
jimthompson5910 (jim_thompson5910):
not quite
jimthompson5910 (jim_thompson5910):
what two numbers multiply to 8 and add to -6
OpenStudy (anonymous):
what??? what two numbers multiply to 8 and add to -6???? thats is confusing i dont understand the way you worded it
jimthompson5910 (jim_thompson5910):
list the factors of 8
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OpenStudy (anonymous):
4 and 2
OpenStudy (anonymous):
so the second part of step 3 is??
OpenStudy (anonymous):
x(2-x)(???)
OpenStudy (anonymous):
(8-6)???
jimthompson5910 (jim_thompson5910):
so we get (2-x)(4-x)
which means that the missing part is (4-x)
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jimthompson5910 (jim_thompson5910):
the complete factorization is x(2-x)(4-x)
OpenStudy (anonymous):
umm how do i factor these
jimthompson5910 (jim_thompson5910):
it's already factored
jimthompson5910 (jim_thompson5910):
x^3 - 6x^2 + 8x
factors to
x(2-x)(4-x)
OpenStudy (anonymous):
yea im not understanding i dont even see how we got x(2-x)(4-x)
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jimthompson5910 (jim_thompson5910):
x^3 - 6x^2 + 8x
x(x^2-6x+8)
we then factor x^2-6x+8 into (2-x)(4-x) and this means
x^3 - 6x^2 + 8x factors to x(2-x)(4-x)