Question

Factor the following polynomial completely,

Answer 1

Answer:

OPTION C

Step-by-step explanation:

The given polynomial is: 1280 x¹¹ - 405 x⁷.

The least power of the variable is taken common outside. So we get:

x⁷{1280 x⁴ - 405}

Now, 5 is a factor of both 1280 and 405.

So, it can be written as:

5x⁷{256x⁴ - 81}

We know that $a^2 - b^2 = (a + b)(a - b)$

Also, 256 = 16² and 81 = 9².

Therefore, this can be rewritten as: $5x^7 \{(16x^2)^2 - 9^2\}$

Using the above formula, a = 16x² and b = 9.

Therefore, this becomes: $5x^7 \{ (16x^2 - 9) (16x^2 + 9)\}$

$(16x^2 - 9)$ can again be factorized with a = 16x and b = 3.

Therefore, it would be: $5x^7 \{ (4x + 3)(4x - 3) (16x^2 + 9)\}$

Hence, OPTION C is the answer.

Answer 2

Answer:

Option C

Step-by-step explanation:

The given polynomial is: 1280 x¹¹ - 405 x⁷.

The least power of the variable is taken common outside. So we get:

x⁷{1280 x⁴ - 405}

Now, 5 is a factor of both 1280 and 405.

So, it can be written as:

5x⁷{256x⁴ - 81}

We know that

Also, 256 = 16² and 81 = 9².

Therefore, this can be rewritten as:

Using the above formula, a = 16x² and b = 9.

Therefore, this becomes:

can again be factorized with a = 16x and b = 3.

Therefore, it would be:

Hence, OPTION C is the answer.

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