Question

(x-2)is factor of (x3-8)

Answer 1

Hi friend ✋✋✋✋
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Your answer
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To verify : - (x - 2) is af factor of (x³ - 8) .

Now,
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x³ - 8

=> (x)³ - (2)³

=> (x - 2)(x² + 2x + 4) [ using identity a³ - b³ = (a - b)(a² + ab + b²)]

Therefore,
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yes , (x - 2) is a factor of (x³ - 8) .

HOPE IT HELPS

Answer 2

Answer:

Yes, $(x-2)$ is a factor of (x³ - 8).

Step-by-step explanation:

Recall the identity,

a³ - b³ = (a - b)(a² + ab + b²) _____ (1)

Step 1 of 1

To show:-

$(x - 2)$ is a factor of (x³ - 8).

Consider the given polynomial as follows:

(x³ - 8)

Rewrite the polynomial as follows:

x³ - 2³

Now, let a = x and b = 2.

Substitute the values of a and b in the equation (1) as follows:

x³ - 2³ = $(x - 2)$(x² + x(2) + 2²)

Simplify as follows:

x³ - 8 = $(x - 2)$(x² + 2x + 4)

Notice that the term (x - 2) is a factor of (x³ - 8).

Therefore, $(x-2)$ is a factor of (x³ - 8) is proved.

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