Answer

Verified

372.6k+ views

**Hint:**(1) The term factor by grouping then we have to factor out common factors. Then we have to compare the given equation in the standard form, i.e. $a{{x}^{2}}+bx+c$

(2) Then we have to substitute the given equation in standard form. But here the equation started with the cubic term. So, you need to do this by grouping the first two terms with each other and the second term with each other.

(3) After that take out the common factor from it you get the factor by the factor by grouping.

**Complete step by step solution:**Here we have,

Here,

We have the equation,

${{x}^{3}}+3{{x}^{2}}+6x+18$

The equation shows that the ratio between the first and second terms are the same as that between the third and fourth term.

Then we can say that the method we use here is factor by grouping to solve problems.

${{x}^{3}}+3{{x}^{2}}+6x+18$

Now,

[Grouping the first two terms with each other and second term with each other]

We get,

${{x}^{3}}+3{{x}^{2}}+6x+18=\left( {{x}^{3}}+3{{x}^{2}} \right)+\left( 6x+18 \right)$ [common factor]

Taking common from brackets.

${{x}^{3}}+3{{x}^{2}}+6x+18={{x}^{2}}\left( x+3 \right)+6\left( x+3 \right)$

$=\left( {{x}^{2}}+6 \right)\left( x+3 \right)$

Hence,

By factor by grouping we get the factor $\left( {{x}^{2}}+6 \right)\left( x+3 \right)$

**Additional Information:**

(1) Factoring in a polynomial has writing it as a product of two or more polynomials.

(2) In the method of factorisation we reduce it in simplex form. The factor can be an integer, a variable or algebraic itself in any type of equation.

(3) There are various methods of factorisation. They are factoring out GCF, the grouping method, the difference of square pattern etc.

(4) We have several example of factoring, However for this you should taking common factor using distributive property.

For example: $6{{x}^{2}}+4x=2x\left( 3x+2 \right)$

**Note:**

(1) To use a grouping method we have to group the expression in two groups. As we have two groups factor out the GCF from the given groups.

(2) If you solve this type of equation the binomial which is in the parenthesis must be the same, if it is not the same then there should be any mistake in the factor.

(3) you should also check the sign properly while writing the final answer.

Recently Updated Pages

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Name 10 Living and Non living things class 9 biology CBSE

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

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail