Math, asked by usama32230, 4 months ago

(x^3+19x-30) Divide by
(x^2-3x-10)

Answers

Answered by shraddha974096
2

Answer:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

STEP

1

:

           x3 - 19x - 30

Simplify   —————————————

           x2 - 3x - 10  

Polynomial Roots Calculator :

1.1    Find roots (zeroes) of :       F(x) = x3 - 19x - 30

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  -30.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,5 ,6 ,10 ,15 ,30

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -12.00      

     -2       1        -2.00        0.00      x + 2  

     -3       1        -3.00        0.00      x + 3  

     -5       1        -5.00        -60.00      

     -6       1        -6.00        -132.00      

     -10       1       -10.00        -840.00      

     -15       1       -15.00       -3120.00      

     -30       1       -30.00       -26460.00      

     1       1        1.00        -48.00      

     2       1        2.00        -60.00      

     3       1        3.00        -60.00      

     5       1        5.00        0.00      x - 5  

     6       1        6.00        72.00      

     10       1        10.00        780.00      

     15       1        15.00        3060.00      

     30       1        30.00       26400.00      

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

  x3 - 19x - 30  

can be divided by 3 different polynomials,including by  x - 5  

Polynomial Long Division :

1.2    Polynomial Long Division

Dividing :  x3 - 19x - 30  

                             ("Dividend")

By         :    x - 5    ("Divisor")

dividend     x3      -  19x  -  30  

- divisor  * x2     x3  -  5x2          

remainder         5x2  -  19x  -  30  

- divisor  * 5x1         5x2  -  25x      

remainder             6x  -  30  

- divisor  * 6x0             6x  -  30  

remainder                0

Quotient :  x2+5x+6  Remainder:  0  

Trying to factor by splitting the middle term

1.3     Factoring  x2+5x+6  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +5x  its coefficient is  5 .

The last term, "the constant", is  +6  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 6 = 6  

Step-2 : Find two factors of  6  whose sum equals the coefficient of the middle term, which is   5 .

     -6    +    -1    =    -7  

     -3    +    -2    =    -5  

     -2    +    -3    =    -5  

     -1    +    -6    =    -7  

     1    +    6    =    7  

     2    +    3    =    5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  3  

                    x2 + 2x + 3x + 6

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+2)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x+2)

Step-5 : Add up the four terms of step 4 :

                   (x+3)  •  (x+2)

            Which is the desired factorization

Trying to factor by splitting the middle term

1.4     Factoring  x2-3x-10  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -3x  its coefficient is  -3 .

The last term, "the constant", is  -10  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -10 = -10  

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   -3 .

     -10    +    1    =    -9  

     -5    +    2    =    -3    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  2  

                    x2 - 5x + 2x - 10

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-5)

             Add up the last 2 terms, pulling out common factors :

                   2 • (x-5)

Step-5 : Add up the four terms of step 4 :

                   (x+2)  •  (x-5)

            Which is the desired factorization

Canceling Out :

1.5    Cancel out  (x+2)  which appears on both sides of the fraction line.

Canceling Out :

1.6    Cancel out  (x-5)  which appears on both sides of the fraction line.

Final result :

 x + 3

Step-by-step explanation:

Answered by pkm1237
0

Answer:

sorry i don't no................,

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