Explanation

HCF = x - 2

LCM = x^3 + 3x^2 - 6x - 8

One polynomial = x^2 - x - 2 = (x - 2)(x + 1)

Factorize LCM:

x^3 + 3x^2 - 6x - 8 = (x - 2)(x^2 + 5x + 4) = (x - 2)(x + 1)(x + 4)

Using HCF × LCM = Product of polynomials:

(x - 2) × (x - 2)(x + 1)(x + 4) = (x - 2)(x + 1) × Second polynomial

Second polynomial = (x - 2)(x + 4) = x^2 + 2x - 8

Explanation

In negative sentences, we use "anything" instead of "something" or "nothing."

The phrase "we cannot do anything about it" is grammatically correct.

Explanation

A biographical essay about a deceased person is usually written in the past tense.

This is because it describes events and actions that have already happened in the person's life.

Explanation

The respiratory system is responsible for supplying oxygen to the blood and removing carbon dioxide from the body.

Key organs include the lungs, trachea, and diaphragm, which help in breathing and gas exchange.

Explanation

To find when both grades visit the lab on the same day again, we need to find the Least Common Multiple (LCM) of 16 and 30.

Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240

Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240

The LCM of 16 and 30 is 240.

Explanation

Epiphytes grow on large trees to access sunlight but do not harm the host tree or take nutrients from it.

This is an example of commensalism, where one organism benefits and the other is unaffected.

Explanation

Given:

∪ = {1, 2, 3, ..., 15}

A = {2, 4, 6, ..., 14}

B = {1, 3, 5, ..., 15}

A' = ∪ - A = {1, 3, 5, ..., 15} = B

B' = ∪ - B = {2, 4, 6, ..., 14} = A

A' ∪ B' = B ∪ A = ∪ (since B and A are complementary sets that together form ∪)

Explanation

"Lying" is the present participle of "lie" (to recline), used here as a continuous action.

The sentence describes people reclining on the sofa while watching TV, so "Lying" fits grammatically.

Explanation

In 1971, during the Indo-Pak war, the 7th American Fleet (Marine Craft) moved toward East Pakistan (now Bangladesh).

Its purpose was to show support for Pakistan, but it did not engage militarily in the conflict.

Explanation

Measurement refers to the quantitative assessment of a student's performance, often in numbers or scores.

The example "Farhan solved 23 out of 40 problems" is a numerical description, making it a clear case of measurement.