## anonymous 5 years ago 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

1. amistre64

divide it thru?

2. amistre64

if its got no remainder its a factor

3. amistre64

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

4. amistre64

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

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. amistre64

:)

11. anonymous

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

12. anonymous

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

13. anonymous

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

14. anonymous

115 to go and then i quit!

15. amistre64

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

16. anonymous

Thank you