Answer
397.8k+ views
Hint: Here we will factorize the given polynomial by using the factor theorem. First, we will find a value of \[x\] which satisfies the polynomial by hit and trial method. Then we will take that factor and divide the polynomial by it, to find the next set of factors.
Complete step-by-step answer:
We have to factorize polynomials \[{x^2} - 3x\].
First, we need to know at least one zero of the polynomial, so we will use the hit and trial method.
Let us check whether \[x = 0\] satisfies the polynomial or not.
Putting \[x = 0\] in \[{x^2} - 3x\], we get,
\[{0^2} - 3 \times 0 = 0\]
So \[x = 0\] is a factor as it satisfies the polynomial.
So, one factor is \[\left( {x - 0} \right)\] or we can say \[x\] is the factor of the given polynomial.
Now we will divide the polynomial \[{x^2} - 3x\] by \[x\] and take out the common term from both the terms of the polynomial. Therefore, we get
\[\dfrac{{{x^2} - 3x}}{x} = \dfrac{{x\left( {x - 3} \right)}}{x}\]
Cancelling out the common terms, we get
\[ \Rightarrow \dfrac{{{x^2} - 3x}}{x} = \left( {x - 3} \right)\]
So, we get the quotient as \[\left( {x - 3} \right)\].
So, we get the zeroes of the given polynomial as \[x = 3\].
Hence, the factors of the polynomial are \[\left( x \right)\left( {x - 3} \right)\]
Note:
Factor theorem states that if a polynomial \[f\left( x \right)\] of degree \[n \ge 1\] and ‘\[a\]’ is any real number then, if \[f\left( a \right) = 0\] then only \[\left( {x - a} \right)\] is a factor of the polynomial. The two problems where Factor Theorem is usually applied are when we have to factorize a polynomial and also when we have to find the roots of the polynomial. It is also used to remove known zeros from a polynomial while leaving all unknown zeros intact. It is a special case of a polynomial remainder theorem.
Complete step-by-step answer:
We have to factorize polynomials \[{x^2} - 3x\].
First, we need to know at least one zero of the polynomial, so we will use the hit and trial method.
Let us check whether \[x = 0\] satisfies the polynomial or not.
Putting \[x = 0\] in \[{x^2} - 3x\], we get,
\[{0^2} - 3 \times 0 = 0\]
So \[x = 0\] is a factor as it satisfies the polynomial.
So, one factor is \[\left( {x - 0} \right)\] or we can say \[x\] is the factor of the given polynomial.
Now we will divide the polynomial \[{x^2} - 3x\] by \[x\] and take out the common term from both the terms of the polynomial. Therefore, we get
\[\dfrac{{{x^2} - 3x}}{x} = \dfrac{{x\left( {x - 3} \right)}}{x}\]
Cancelling out the common terms, we get
\[ \Rightarrow \dfrac{{{x^2} - 3x}}{x} = \left( {x - 3} \right)\]
So, we get the quotient as \[\left( {x - 3} \right)\].
So, we get the zeroes of the given polynomial as \[x = 3\].
Hence, the factors of the polynomial are \[\left( x \right)\left( {x - 3} \right)\]
Note:
Factor theorem states that if a polynomial \[f\left( x \right)\] of degree \[n \ge 1\] and ‘\[a\]’ is any real number then, if \[f\left( a \right) = 0\] then only \[\left( {x - a} \right)\] is a factor of the polynomial. The two problems where Factor Theorem is usually applied are when we have to factorize a polynomial and also when we have to find the roots of the polynomial. It is also used to remove known zeros from a polynomial while leaving all unknown zeros intact. It is a special case of a polynomial remainder theorem.
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)