Question

divide x*4+6x*3+x*2-24x-20 by x*2+3x-10
​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

x = 5

x = 2

x = 1

x = -2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((((x4) -  (2•3x3)) +  x2) +  24x) -  20  = 0  

Step  2  :

Polynomial Roots Calculator :

2.1    Find roots (zeroes) of :       F(x) = x4-6x3+x2+24x-20

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  1  and the Trailing Constant is  -20.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,4 ,5 ,10 ,20

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -36.00      

     -2       1        -2.00        0.00      x+2  

     -4       1        -4.00        540.00      

     -5       1        -5.00        1260.00      

     -10       1       -10.00       15840.00      

     -20       1       -20.00       207900.00      

     1       1        1.00        0.00      x-1  

     2       1        2.00        0.00      x-2  

     4       1        4.00        -36.00      

     5       1        5.00        0.00      x-5  

     10       1        10.00        4320.00      

     20       1        20.00       112860.00      

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

  x4-6x3+x2+24x-20  

can be divided by 4 different polynomials,including by  x-5  

Polynomial Long Division :

2.2    Polynomial Long Division

Dividing :  x4-6x3+x2+24x-20  

                             ("Dividend")

By         :    x-5    ("Divisor")

dividend     x4  -  6x3  +  x2  +  24x  -  20  

- divisor  * x3     x4  -  5x3              

remainder      -  x3  +  x2  +  24x  -  20  

- divisor  * -x2      -  x3  +  5x2          

remainder          -  4x2  +  24x  -  20  

- divisor  * -4x1          -  4x2  +  20x      

remainder                 4x  -  20  

- divisor  * 4x0                 4x  -  20  

remainder                    0

Quotient :  x3-x2-4x+4  Remainder:  0  

Polynomial Roots Calculator :

2.3    Find roots (zeroes) of :       F(x) = x3-x2-4x+4

    See theory in step 2.1

In this case, the Leading Coefficient is  1  and the Trailing Constant is  4.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,4

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        6.00      

     -2       1        -2.00        0.00      x+2  

     -4       1        -4.00        -60.00      

     1       1        1.00        0.00      x-1  

     2       1        2.00        0.00      x-2  

     4       1        4.00        36.00      

Step-by-step explanation: