Polynomial Long Division 17x^3 - 22x + 7x^4 + 24

Using polynomial long division, evaluate the expression below:

17x3 - 22x + 7x4 + 24 - 47x2

7x - 4

First, we write our expression in long division format and follow the steps below.

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Step 1
 1a)  Divide the first term of the dividend by the first term of the divisor → 7x⁴ ÷ 7x = 1x^{(4 - 1)} = x³
 1b)  We multiply that part of the quotient by the divisor → x³(7x - 4) = 7x⁴ - 4x³  →  Click here to see the Math for this Multiplication.
 1c)  Subtract 7x⁴ - 4x³ from 7x⁴ + 17x³ - 47x² - 22x + 24 to get 21x³ - 47x² - 22x + 24  →  Click here to see the Math.

x3

7x

-

4

7x4

+

17x3

-

47x2

-

22x

+

24

7x4

-

4x3

21x3

-

47x2

-

22x

+

24

---

Step 2
 2a)  Divide the first term of the dividend by the first term of the divisor → 21x³ ÷ 7x = 3x^{(3 - 1)} = 3x²
 2b)  We multiply that part of the quotient by the divisor → 3x²(7x - 4) = 21x³ - 12x²  →  Click here to see the Math for this Multiplication.
 2c)  Subtract 21x³ - 12x² from 21x³ - 47x² - 22x + 24 to get -35x² - 22x + 24  →  Click here to see the Math.

x3

+

3x2

7x

-

4

7x4

+

17x3

-

47x2

-

22x

+

24

7x4

-

4x3

21x3

-

47x2

-

22x

+

24

21x3

-

12x2

-35x2

-

22x

+

24

---

Step 3
 3a)  Divide the first term of the dividend by the first term of the divisor → -35x² ÷ 7x = -5x^{(2 - 1)} = -5x
 3b)  We multiply that part of the quotient by the divisor → -5x(7x - 4) = -35x² + 20x  →  Click here to see the Math for this Multiplication.
 3c)  Subtract -35x² + 20x from -35x² - 22x + 24 to get -42x + 24  →  Click here to see the Math.

x3

+

3x2

-

5x

7x

-

4

7x4

+

17x3

-

47x2

-

22x

+

24

7x4

-

4x3

21x3

-

47x2

-

22x

+

24

21x3

-

12x2

-35x2

-

22x

+

24

-35x2

+

20x

-42x

+

24

---

Step 4
 4a)  Divide the first term of the dividend by the first term of the divisor → -42x ÷ 7x = -6x^{(1 - 1)} = -6
 4b)  We multiply that part of the quotient by the divisor → -6(7x - 4) = -42x + 24  →  Click here to see the Math for this Multiplication.
 4c)  Subtract -42x + 24 from -42x + 24 to get   →  Click here to see the Math.

x3

+

3x2

-

5x

-

6

7x

-

4

7x4

+

17x3

-

47x2

-

22x

+

24

7x4

-

4x3

21x3

-

47x2

-

22x

+

24

21x3

-

12x2

-35x2

-

22x

+

24

-35x2

+

20x

-42x

+

24

-42x

+

24

---

Since we do not have a remainder, we have our answer below:
Answer = x³ + 3x² - 5x - 6

Answer = x³ + 3x² - 5x - 6

You have 1 free calculations remaining

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What is the Answer?

Answer = x³ + 3x² - 5x - 6

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math operation involving the difference of elements

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