Answer
396.9k+ views
Hint: Given polynomial is of degree 2. Polynomials of degree 2 are known as Quadratic polynomials. Quadratic polynomials can be factored by the help of splitting the middle term method. In this method, the middle term is split into two terms in such a way that the polynomial remains unchanged.
Complete step-by-step solution:
For factorising the given quadratic polynomial $\left( {3{x^2} - 5x - 2} \right)$ , we can use the splitting method in which the middle term is split into two terms such that the sum of the terms gives us the original middle term and product of the terms gives us the product of the constant term and coefficient of ${x^2}$.
So, $\left( {3{x^2} - 5x - 2} \right)$
$ = $$3{x^2} - \left( {6 - 1} \right)x - 2$
We split the middle term $ - 5x$ into two terms $ - 6x$ and $x$ since the product of these terms, $ - 6{x^2}$ is equal to the product of the constant term and coefficient of ${x^2}$ and sum of these terms gives us the original middle term, $ - 5x$.
$ = $$3{x^2} - 6x + x - 2$
$ = $\[3x\left( {x - 2} \right) + \left( {x - 2} \right)\]
$ = $\[\left( {3x + 1} \right)\left( {x - 2} \right)\]
So, the factored form of the quadratic polynomial $\left( {3{x^2} - 5x - 2} \right)$ is \[\left( {3x + 1} \right)\left( {x - 2} \right)\].
Note: Splitting of the middle term can be a tedious process at times when the product of the constant term and coefficient of ${x^2}$ is a large number with a large number of divisors. Special care should be taken in such cases. Similar to quadratic polynomials, quadratic equations can also be solved using factorisation methods. Besides factorisation, there are various methods to solve quadratic equations such as completing the square method and using the Quadratic formula.
Complete step-by-step solution:
For factorising the given quadratic polynomial $\left( {3{x^2} - 5x - 2} \right)$ , we can use the splitting method in which the middle term is split into two terms such that the sum of the terms gives us the original middle term and product of the terms gives us the product of the constant term and coefficient of ${x^2}$.
So, $\left( {3{x^2} - 5x - 2} \right)$
$ = $$3{x^2} - \left( {6 - 1} \right)x - 2$
We split the middle term $ - 5x$ into two terms $ - 6x$ and $x$ since the product of these terms, $ - 6{x^2}$ is equal to the product of the constant term and coefficient of ${x^2}$ and sum of these terms gives us the original middle term, $ - 5x$.
$ = $$3{x^2} - 6x + x - 2$
$ = $\[3x\left( {x - 2} \right) + \left( {x - 2} \right)\]
$ = $\[\left( {3x + 1} \right)\left( {x - 2} \right)\]
So, the factored form of the quadratic polynomial $\left( {3{x^2} - 5x - 2} \right)$ is \[\left( {3x + 1} \right)\left( {x - 2} \right)\].
Note: Splitting of the middle term can be a tedious process at times when the product of the constant term and coefficient of ${x^2}$ is a large number with a large number of divisors. Special care should be taken in such cases. Similar to quadratic polynomials, quadratic equations can also be solved using factorisation methods. Besides factorisation, there are various methods to solve quadratic equations such as completing the square method and using the Quadratic formula.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)