Question

decide using the factor theorem whether x minus 2 is factor of x cube minus 4 x square - 4

Answer 1

Answer:

Step-by-step explanation:

p(x)=x³- 4x ² -4

Putting x=2

P(2)= 8-16-4

       =8-20

      =-12

Therefore x-2 is not a factor of P(x)

Answer 2

x - 2 is not a factor of given polynomial

Solution:

Given equation is:

$x^3 - 4x^2 - 4$

Factor theorem:

If "x = a" is a factor of f(x), then f(a) = 0

Given that,

x - 2 is a factor

Then,

f(2) = 0

Check if f(2) = 0

$f(2) = 2^3 - 4(2)^2 -4\\\\f(2) = 8 - 4 \times 4 - 4\\\\f(2) = 8 - 16 - 4\\\\f(2) = -12\\\\Thus\\\\f(2)\neq 0$

Therefore, x - 2 is not a factor of given polynomial

Learn more about this topic

Using the factor theorem, show that (x - 2) is a factor of x3 + x2 - 4x - 4.

Hence factorise the polynomial completely.​

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Using factor theorem show that a-b,b-c and c-a are the factors of a(b^2-c^2)+b(c^2-a^2)+c(a^2-b^2)

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