mysteryinc2002
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PLEASE HELP!!!!

Simplify the expression (x^4+4x^3-5x-20)÷(x+4) using synthetic division. After doing the synthetic division, which gives you just coefficients. Convert the coefficient quotient answer, into a polynomial with variable x and the correct exponent powers in it. Convert your coefficient answer into a polynomial.

Hint: remember to fill in any missing degree terms in your dividend with coefficients that are zero to represent missing place holders.

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joseaaronlara

Answer:

The answer to your question is:  (x³ - 5) (x + 4)

Step-by-step explanation:

x⁴ + 4x³ - 5x - 20      /     x + 4                x = -4

                  1     4     0     -5     -20           -4

                      -4       0     0    +20

                   1    0      0    -5       0        =   x³ - 5

Finally   (x³ - 5) (x + 4) = x⁴ + 4x³ - 5x - 20

           

Answer:

Step-by-step explanation:

Given is an algebraic expression as

[tex](x^4+4x^3-5x-20)[/tex]

which is to be divided by [tex]x+4[/tex]

Method to be used: synthetic division

We write the coefficients of the dividend in descending order with 0 for non existing x term

So this would be as

1      4       0    -5   -20

Divisor equate to 0 to get

[tex]x+4=0\\x=-4[/tex]

So we write -4 on the left side and do synthetic division.  Synthetic division is writing I term as it is, and next step is to multiply the I term answer by -4 and write below II term.  Now add the 2 terms in II column and continue this till the last term

-4   |   1      4     0   -5     -20

     |           -4    0    0      20

     |__________________

          1      0     0    -5       0=Remainder

Hence we find right most answer as remainder =0

Quotient is

[tex]x^3-5[/tex](writing from left most with powers of x in descending powers)

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