anonymous
  • anonymous
How do you use the Factor Theorem to show that the second polynomial is a factor of the first polynomial? 2x^3 - 5x^2 + 6x - 2, x - 1/2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
divide it thru?
amistre64
  • amistre64
if its got no remainder its a factor
amistre64
  • amistre64
.5| 2 -5 6 -2 0 1 -2 2 ------------ 2 -4 4 0 <- remainder 0, its a factor

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amistre64
  • amistre64
cant really say that I know what a factor therom is tho ...
anonymous
  • anonymous
factor theorem sez that if r is a zero of a polynomial \[p(x)\] then \[p(x)=(x-r)q(x)\]
anonymous
  • anonymous
so if you know \[p(\frac{1}{2})=0\] then you know \[p(x)=(x-\frac{1}{2})q(x)\]
anonymous
  • anonymous
if f(1/2) is equal to zero then x-1/2 is a factot
anonymous
  • anonymous
more easily written as \[p(x)=( 2x-1)q(x)\]
anonymous
  • anonymous
amistre as usual did all the work, so you even know what \[q(x)\] is
amistre64
  • amistre64
:)
anonymous
  • anonymous
it is \[2x^2-4x+4=2(x^2+2x+2)\]
anonymous
  • anonymous
so your polynomial is \[p(x)=(2x-1)(x^2-2x+2)\]
anonymous
  • anonymous
oops typo in other answer . it is -2x not +2x sorry
anonymous
  • anonymous
115 to go and then i quit!
amistre64
  • amistre64
\(\left(\begin{array}ca&b&c\\d&e&f\\g&h&i \end{array} \right)\)
anonymous
  • anonymous
Thank you

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