Math, asked by PrinceBrar, 1 year ago

divide the polynomial 2x^4+7x^3+4x^2-7x-9

Answers

Answered by yuvrajrathore
0
Step by step solution :Step  1  :Equation at the end of step  1  : ((((2•(x4))-(7•(x3)))+32x2)-7x)+2 = 0 Step  2  :Equation at the end of step  2  : ((((2•(x4))-7x3)+32x2)-7x)+2 = 0 Step  3  :Equation at the end of step  3  : (((2x4 - 7x3) + 32x2) - 7x) + 2 = 0 Step  4  :Polynomial Roots Calculator :

 4.1    Find roots (zeroes) of :       F(x) = 2x4-7x3+9x2-7x+2
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q  then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  2  and the Trailing Constant is  2. 

 
The factor(s) are: 

of the Leading Coefficient :  1,2 
 
of the Trailing Constant :  1 ,2 

 
Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      27.00        -1     2      -0.50      8.75        -2     1      -2.00      140.00        1     1      1.00      -1.00        1     2      0.50      0.00    2x-1      2     1      2.00      0.00    x-2 


The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms 

In our case this means that 
   2x4-7x3+9x2-7x+2 
can be divided by 2 different polynomials,including by  x-2 


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