Example Question - quotient and remainder
Here are examples of questions we've helped users solve.
Dividing a Cubic Polynomial by a Linear Monomial
Given \( P(x) = 2x^3 + 3x^2 - x - 5 \) and \( D(x) = x - 1 \), we will perform polynomial long division. \[ \begin{array}{r} 2x^2+5x+4 \\ x-1 \,|\overline{\, 2x^3 + 3x^2 - x - 5} \\ -\underline{2x^3 - 2x^2} \\ 5x^2 - x \\ -\underline{5x^2 - 5x} \\ 4x - 5 \\ -\underline{4x - 4} \\ -1 \end{array} \] The quotient is \( Q(x) = 2x^2 + 5x + 4 \) and the remainder is \( -1 \).
Long Division: Finding Quotient and Remainder for 8,489 ÷ 9
The image shows a division problem, asking to find the quotient of the division of 8,489 by 9. Let's solve the problem using long division: ``` 8,489 ÷ 9 ``` First, we see how many times 9 fits into 84 (the first two digits of 8,489), since 9 doesn't fit into 8: ```plaintext 9 ) 8,489 - 72 ------ 148 ``` 9 fits into 84 a total of 9 times (9 x 9 = 81) with a remainder of 3. We bring down the next digit which is 8, making it 148. Now we see how many times 9 fits into 148: ```plaintext 9 ) 8,489 - 72 ------ 148 - 135 ------ 13 ``` 9 fits into 148 a total of 16 times (9 x 16 = 144) with a remainder of 4. We bring down the last digit which is 9, making it 139. Finally, we see how many times 9 fits into 139: ```plaintext 9 ) 8,489 - 72 ------ 148 - 144 ------ 139 - 135 ------ 4 ``` 9 fits into 139 a total of 15 times (9 x 15 = 135) with a remainder of 4. Therefore, the quotient of 8,489 divided by 9 is 943 with a remainder of 4, or 943 R4.
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