A point is zero-dimensional with respect to the covering dimension because every open cover of the space has a refinement consisting of a single open set.

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3 years ago

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The binomial 5x – 4 is a factor of 10x2 – 23x + 12. What is the other factor?

SVETLANKA909090 [29]

$Method\ 1^o\\10x^2-23x+12=(5x-4)(ax+b)\\\\10x^2-23x+12=5ax^2+5bx-4ax-4b\\\\10x^2-23x+12=5ax^2+(5b-4a)x-4b\\\\therefore\\\\ \begin{array}{ccc}(1)\\(2)\\(3)\end{array}\left\{\begin{array}{ccc}5a=10\\5b-4a=-23\\-4b=12\end{array}\right\\\\(1)\ divide\ both\ sides\ by\ 5\to a=2\\(3)\ divide\ both\ sides\ by\ (-4)\to b=-3\\check\\subtitute\ the\ values\ of\ "a"\ and\ "b"\ to\ (2):\\5\cdot(-3)-4\cdot2=-15-8=-23\ /correct/\\\\Answer:\boxed{2x-3}$

$Method\ 2^o\\10x^2-23x+12=10x^2-8x-15x+12\\=2x\cdot5x-2x\cdot4-3\cdot5x-3\cdot(-4)\\=2x(5x-4)-3(5x-4)=(5x-4)\boxed{(2x-3)}$

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3 years ago