Answer

Verified

447k+ views

**Hint:**find the factor or rather factorize them. The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.

Formula and

\[\begin{align}

& {{a}^{2}}-{{b}^{2}}=(a-b)(a+b) \\

& {{a}^{3}}-{{b}^{3}}=(a-b)({{a}^{2}}-ab+{{b}^{2}}) \\

& {{a}^{3}}+{{b}^{3}}=(a-b)({{a}^{2}}-ab+{{b}^{2}}) \\

\end{align}\]

Also we can add ${{a}^{3}}-{{b}^{3}}={{(a-b)}^{3}}+3{{a}^{2}}b-3a{{b}^{2}}$

**Complete step by step solution:**In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, and is a factorization of the polynomial x² – 4.

$({{x}^{2}}-9);\,({{x}^{3}}-27)\,.\,\text{and}\,({{x}^{2}}-8x+15).({{x}^{2}}-9)$

So, this is the given part to which we have to find the Hcf

So, using the formula $[{{a}^{2}}-{{b}^{2}}=(a-b)(a+b)]$

We have

\[\begin{align}

& {{x}^{2}}-9 \\

& \Rightarrow {{x}^{2}}-{{3}^{2}}=(x-3)(x+3) \\

\end{align}\]

Also, using the formula ${{a}^{3}}-{{b}^{3}}=(a-b)({{a}^{2}}-ab+{{b}^{2}})$

We have

\[\begin{align}

& {{x}^{3}}-27 \\

& \Rightarrow {{x}^{3}}-33=(x-3)({{x}^{2}}-2x+3) \\

\end{align}\]

Now, if we factorize ${{x}^{2}}-8x+15$

We get

\[\begin{align}

& {{x}^{2}}-8x+15={{x}^{2}}-5x-3x+15 \\

& =x(x-5)-3(x-5) \\

& =(x-3)(x-5)

\end{align}\]

Therefore, we can see $(x-3)$is the only common factor in $({{x}^{2}}-9),\,({{x}^{2}}-27)({{x}^{2}}-8x+15)$

Hence the HCF for this question is $(x-3)$

**Therefore option (A) is the correct answer.**

**Note:**In this type of question, factorization is must know, find factors then see for the common factors and as HCF suggest the common factor is the HCF of the question. The highest common factor is found by multiplying all the factors which appear in both lists: So the HCF of 60 and 72 is 2 × 2 × 3 which is 12. The lowest common multiple is found by multiplying all the factors which appear in either list: So the LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 which is 360.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE