Question

Answer this quickly and i will mark you as a brainliest!
Determine whether the given numbers are factors of the polynomial equation.

( x - 2 ) is a factor of ( x∧3 - 3x² + 4x - 4 )

choices:
- TRUE
- FALSE

Answer 1

ANSWER:

Given:

p (x) [Dividend] = $(x^3 - 3x^2 + 4x - 4)$

g (x) [Divisor] = (x - 2)

To Find:

Whether g (x) is a Factor of p (x) by using the Factor Theorem -

SOLUTION:

Let g (x) = 0

=> x - 2 = 0 => ∴ x = 2

According to the Rule that (x - a) is a Factor of p (x) if p (a) = 0, Consider a as 2. Then, p (2) = 0

$at\:p(2) => x^3 - 3x^2 + 4x - 4\\\\:=> (2)^3 - 3 (2)^2+ 4 (2) - 4\\\\:=>8 - 3(4) + 8 -4\\\\:=> 8 - 12 + 8 - 4\\\\:= 0$

It also agrees with the Second Rule, i.e., if p (a) = 0, (x - a) is a Factor of p (x)

CONCLUSION:

∴ (x - 2) is a Factor of (x^3 - 3x^2 + 4x - 4)

The Given Statement is 'True'

Answer 2

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