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

Question

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

amistre64 · Answer

divide it thru?

amistre64 · Answer

if its got no remainder its a factor

amistre64 · Answer

.5| 2 -5  6 -2
     0  1  -2  2
------------
     2 -4  4 0 <- remainder 0, its a factor

amistre64 · Answer

cant really say that I know what a factor therom is tho ...

anonymous · Answer

factor theorem sez that if r is a zero of a polynomial $$p(x)$$ then 
$$p(x)=(x-r)q(x)$$

anonymous · Answer

so if you know $$p(\frac{1}{2})=0$$ then you know 
$$p(x)=(x-\frac{1}{2})q(x)$$

anonymous · Answer

if f(1/2) is equal to zero then x-1/2 is a factot

anonymous · Answer

more easily written as 
$$p(x)=( 2x-1)q(x)$$

anonymous · Answer

amistre as usual did all the work, so you even know what $$q(x)$$ is

amistre64 · Answer

:)

anonymous · Answer

it is $$2x^2-4x+4=2(x^2+2x+2)$$

anonymous · Answer

so your polynomial is $$p(x)=(2x-1)(x^2-2x+2)$$

anonymous · Answer

oops typo in other answer .  it is -2x not +2x sorry

anonymous · Answer

115 to go and then i quit!

amistre64 · Answer

$\left(\begin{array}ca&b&c\d&e&f\g&h&i \end{array} \right)$

anonymous · Answer

Thank you