Polynomial steps
Introduction:
Polynomial defined as the function p(x) of the form p(x) =a0 +a1x+a2x2+……….anxn. Where a0, a1…an real numbers and n is the non negative integers is called polynomial in x over reals. For example 4x2-7x+3 is a polynomial over integers. If one of the powers of x in p(x) is either a negative integer of a fraction (either positive or negative), then p(x) is not a polynomial. For example x+2/x is not a polynomial. The highest exponent of the variable in polynomial is called the degree of the polynomial. Here we are going to study about how to solve the polynomial step by step operation examples.
Steps to performing factor of a polynomial
To find the real roots of the polynomial x2 + 7x +6 =0
Solution:
Step: 1
First we have to find the factor for a given polynomial
We can write
x2 + 7x +6 = (x+1)(x+6)
These are the two factors the equation
Now we solve the both equation.
Step: 2
Both terms equating to zero we get
First x+1=0
Add both sides -1 we get
x=-1
Next term is x+6 = 0
Add both sides -6
x=-6
Step: 3
Therefore the real root of the given polynomial is -1,-6
Steps for writing polynomial in standard form:
Example: 2
Simplify the following and write the result in standard form.
(x + x2 + 2) + (x2 - 2x + 10)
Solution:
Step: 1
First we have to simplify the given polynomial
x+ x2+2+x2-2x+10
Combining Like Terms x2
x2+x2 = 2x2
Combine the next like term x
x- 2x = -x
Combine the constant
2+10 =12
Step: 2
Now we write into standard form that is write largest degree to lowest degree
2x2-x+12
Therefore the final answer is 2x2-x+12
Polynomial defined as the function p(x) of the form p(x) =a0 +a1x+a2x2+……….anxn. Where a0, a1…an real numbers and n is the non negative integers is called polynomial in x over reals. For example 4x2-7x+3 is a polynomial over integers. If one of the powers of x in p(x) is either a negative integer of a fraction (either positive or negative), then p(x) is not a polynomial. For example x+2/x is not a polynomial. The highest exponent of the variable in polynomial is called the degree of the polynomial. Here we are going to study about how to solve the polynomial step by step operation examples.
Steps to performing factor of a polynomial
- First we have to find the factor of a given polynomial
- Then equating the factor to zero
- Find the real roots for the given polynomial.
To find the real roots of the polynomial x2 + 7x +6 =0
Solution:
Step: 1
First we have to find the factor for a given polynomial
We can write
x2 + 7x +6 = (x+1)(x+6)
These are the two factors the equation
Now we solve the both equation.
Step: 2
Both terms equating to zero we get
First x+1=0
Add both sides -1 we get
x=-1
Next term is x+6 = 0
Add both sides -6
x=-6
Step: 3
Therefore the real root of the given polynomial is -1,-6
Steps for writing polynomial in standard form:
Example: 2
Simplify the following and write the result in standard form.
(x + x2 + 2) + (x2 - 2x + 10)
Solution:
Step: 1
First we have to simplify the given polynomial
x+ x2+2+x2-2x+10
Combining Like Terms x2
x2+x2 = 2x2
Combine the next like term x
x- 2x = -x
Combine the constant
2+10 =12
Step: 2
Now we write into standard form that is write largest degree to lowest degree
2x2-x+12
Therefore the final answer is 2x2-x+12