Question

Determine if x - 2 is a factor of p(x) = x4 - 3x2 + 2x - 8, and explain why.

Answer 1

Answer:

If x-2 is a factor of p(x) = x^{4} - 3 x^{2} + 2 x - 8 ,then p(x)  = 0

Solution:

According to factor theorem of polynomials,  

x-a is a factor of polynomial p(x), if and only p(a)=0

Step 1:

Since x-2 is factor of p(x),

x - 2 = 0

x = 2

Step 2:

$p(x) = x^{4} - 3 x^{2} + 2 x - 8 ------ (equation 1)$

By substituting x = 2 in equation 1,

$p(x) = 2^{4} - 3(2)^{2} + 2(2) - 8$

p(x) = 16 - 3(4 ) + 4 -8

p(x) = 16 - 12 - 4

p(x) = 16 - 16

p(x) = 0

Since x - 2 is a factor of p(x)  , we get p(x)=0