2x^3+x^2+4 by x-3
Use polynomial long division show word

Question

Manny300303199 · Answer

To divide the polynomial 2x^3 + x^2 + 4 by x - 3 using polynomial long division, follow these steps:

Step 1: Write the division as a fraction using the divisor (x - 3) as the denominator:
     (2x^3 + x^2 + 4)/(x - 3)

Step 2: Divide the leading term of the numerator (2x^3) by the leading term of the divisor (x):
     2x^3 / x = 2x^2

Step 3: Multiply the divisor (x - 3) by the quotient from step 2:
     (x - 3) * 2x^2 = 2x^3 - 6x^2

Step 4: Subtract the result from step 3 from the original numerator:
     (2x^3 + x^2 + 4) - (2x^3 - 6x^2) = 7x^2 + 4

Step 5: Repeat steps 2-4 with the new numerator (7x^2 + 4):
     7x^2 / x = 7x

(x - 3) * 7x = 7x^2 - 21x

(7x^2 + 4) - (7x^2 - 21x) = 25x + 4

Step 6: Repeat steps 2-4 with the new numerator (25x + 4):
     25x / x = 25

(x - 3) * 25 = 25x - 75

(25x + 4) - (25x - 75) = 79

Step 7: The resulting polynomial 79 is the remainder.

Therefore, when dividing 2x^3 + x^2 + 4 by x - 3 using polynomial long division, the quotient is 2x^2 + 7x + 25 and the remainder is 79.

dkononenko072 · Answer

First, set it up like a long division problem:

markdown
Copy code
              2x^2   + 7x    + 21
         _________________________
x - 3  |   2x^3   +  x^2        + 4
Now, divide 
2
�
3
2x 
3
  by 
�
x, which gives 
2
�
2
2x 
2
 , so write 
2
�
2
2x 
2
  above the line, then multiply 
�
−
3
x−3 by 
2
�
2
2x 
2
  and write it beneath the polynomial:

markdown
Copy code
              2x^2   + 7x    + 21
         _________________________
x - 3  |   2x^3   +  x^2        + 4
            2x^3  - 6x^2
Now, subtract 
2
�
3
−
2
�
3
2x 
3
 −2x 
3
  to get 
0
0, and 
�
2
−
(
−
6
�
2
)
x 
2
 −(−6x 
2
 ) to get 
7
�
2
7x 
2
 , so bring down the next term:

markdown
Copy code
              2x^2   + 7x    + 21
         _________________________
x - 3  |   2x^3   +  x^2        + 4
            2x^3  - 6x^2
          _______________
                    7x^2
Now, divide 
7
�
2
7x 
2
  by 
�
x, which gives 
7
�
7x, so write 
7
�
7x above the line, then multiply 
�
−
3
x−3 by 
7
�
7x and write it beneath the polynomial:

markdown
Copy code
              2x^2   + 7x    + 21
         _________________________
x - 3  |   2x^3   +  x^2        + 4
            2x^3  - 6x^2
          _______________
                    7x^2   + 21x
Now, subtract 
7
�
2
−
7
�
2
7x 
2
 −7x 
2
  to get 
0
0, and 
�
2
−
21
�
x 
2
 −21x to get 
21
�
21x, so bring down the next term:

markdown
Copy code
              2x^2   + 7x    + 21
         _________________________
x - 3  |   2x^3   +  x^2        + 4
            2x^3  - 6x^2
          _______________
                    7x^2   + 21x
                    7x^2  - 21x
Now, subtract 
7
�
2
−
7
�
2
7x 
2
 −7x 
2
  to get 
0
0, and 
4
−
(
−
21
�
)
4−(−21x)

curriful · Answer

@dkononenko072 wrote:

First, set it up like a long division problem: markdown Copy code 2x^2 + 7x + 21 _________________________ x - 3 | 2x^3 + x^2 + 4 Now, divide 2 � 3 2x 3 by � x, which gives 2 � 2 2x 2 , so write 2 � 2 2x 2 above the line, then multiply � − 3 x−3 by 2 � 2 2x 2 and write it beneath the polynomial: markdown Copy code 2x^2 + 7x + 21 _________________________ x - 3 | 2x^3 + x^2 + 4 2x^3 - 6x^2 Now, subtract 2 � 3 − 2 � 3 2x 3 −2x 3 to get 0 0, and � 2 − ( − 6 � 2 ) x 2 −(−6x 2 ) to get 7 � 2 7x 2 , so bring down the next term: markdown Copy code 2x^2 + 7x + 21 _________________________ x - 3 | 2x^3 + x^2 + 4 2x^3 - 6x^2 _______________ 7x^2 Now, divide 7 � 2 7x 2 by � x, which gives 7 � 7x, so write 7 � 7x above the line, then multiply � − 3 x−3 by 7 � 7x and write it beneath the polynomial: markdown Copy code 2x^2 + 7x + 21 _________________________ x - 3 | 2x^3 + x^2 + 4 2x^3 - 6x^2 _______________ 7x^2 + 21x Now, subtract 7 � 2 − 7 � 2 7x 2 −7x 2 to get 0 0, and � 2 − 21 � x 2 −21x to get 21 � 21x, so bring down the next term: markdown Copy code 2x^2 + 7x + 21 _________________________ x - 3 | 2x^3 + x^2 + 4 2x^3 - 6x^2 _______________ 7x^2 + 21x 7x^2 - 21x Now, subtract 7 � 2 − 7 � 2 7x 2 −7x 2 to get 0 0, and 4 − ( − 21 � ) 4−(−21x)

mathway?

Manny300303199 · Answer

@curriful wrote:

@dkononenko072 wrote:

First, set it up like a long division problem: markdown Copy code 2x^2 + 7x + 21 _________________________ x - 3 | 2x^3 + x^2 + 4 Now, divide 2 � 3 2x 3 by � x, which gives 2 � 2 2x 2 , so write 2 � 2 2x 2 above the line, then multiply � − 3 x−3 by 2 � 2 2x 2 and write it beneath the polynomial: markdown Copy code 2x^2 + 7x + 21 _________________________ x - 3 | 2x^3 + x^2 + 4 2x^3 - 6x^2 Now, subtract 2 � 3 − 2 � 3 2x 3 −2x 3 to get 0 0, and � 2 − ( − 6 � 2 ) x 2 −(−6x 2 ) to get 7 � 2 7x 2 , so bring down the next term: markdown Copy code 2x^2 + 7x + 21 _________________________ x - 3 | 2x^3 + x^2 + 4 2x^3 - 6x^2 _______________ 7x^2 Now, divide 7 � 2 7x 2 by � x, which gives 7 � 7x, so write 7 � 7x above the line, then multiply � − 3 x−3 by 7 � 7x and write it beneath the polynomial: markdown Copy code 2x^2 + 7x + 21 _________________________ x - 3 | 2x^3 + x^2 + 4 2x^3 - 6x^2 _______________ 7x^2 + 21x Now, subtract 7 � 2 − 7 � 2 7x 2 −7x 2 to get 0 0, and � 2 − 21 � x 2 −21x to get 21 � 21x, so bring down the next term: markdown Copy code 2x^2 + 7x + 21 _________________________ x - 3 | 2x^3 + x^2 + 4 2x^3 - 6x^2 _______________ 7x^2 + 21x 7x^2 - 21x Now, subtract 7 � 2 − 7 � 2 7x 2 −7x 2 to get 0 0, and 4 − ( − 21 � ) 4−(−21x)

mathway?

seems so

Manny300303199 · Answer

@elsa213

shelovejayy · Answer

$$\sqrt[htttt5667^{78}]{?}$$