# x-2 is a factor of p(x)=x to the 3rd power -xto the second power +2x-8Use the factor theoem to tell whether the statement is true or not. If the statement is not true, so indicate

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p(x) = x^3-x^2+2x-8. To check if x-2 is a factor.

Solution:

If x-2 is a factor of p(x), then,

p(x) = (x-2) Q(x) Or

x^3-x^2+2x-8 = (x-2)Q(x), Putting, x= 2,

2^3-2^2+2*2-8 = 0*Q(2). Or

8-4+4-8 = 0 . Or

0 = 0. So fox=2, the equation is satisfied.

Therefore, x-2 is a factor of p(x).

first method

p(x)= X3 -X2 +2X -8

take X = 1,2,3,....................

if x=1,then

p(1)= 1-1+2-8 = -6

till the answer comes 0 repeat this

if x= -1

p(-1)= -1+1-2-8 = -10

if x=2

p(2)= 8-4+4-8 = 0

:. therefore the (X-2) is a factor of p(X)= X3-X2+2X-8

other method

X-2 =0,then

X= +2

if X=2 then

p(X)= (2)3 - (2)2 +2(2) -8 = +8 -4 +4 -8 = 0

therefore the (X-2) is a factor of p(X)= X3-X2+2X-8

p(x)= x^3-x^2+2x-8

(x-2) is a factor??

Solution:

To determine if (x-2) is one of the function's solution, we use the factor theorem. If (x-2) is a factor, then the remainder of dividing p(x) by (x=2) IS ZERO.

Using synthetic division:

2 l 1 -1 2 -8

2 2 8

--------------------------

1 1 4 0

The remainder is 0, then (x-2) is a factor of p(x)

Then the statement is true and the other factor is X^2+x+4

Then P(x) = (x-2)(x^2+x+4)