Need help with answering the quotient and the remainder, (6x^2+35x24)/(x+5)
First of all, your question appears to contain a typo
did you mean:
(6x^2+35x + 24)/(x+5) ??
try this page:
http://calc101.com/webMathematica/long-divide.jsp#topdoit
To find the quotient and remainder of the expression (6x^2+35x+24)/(x+5), you can use polynomial long division. Here's how you can do it step by step:
Step 1: Make sure the expression is written in descending order with respect to the variable. The expression is already in the correct format.
Step 2: Divide the first term of the numerator (6x^2) by the first term of the denominator (x). The result is 6x.
Step 3: Multiply the entire denominator (x+5) by the result from Step 2 (6x). The product is 6x(x+5) = 6x^2 + 30x.
Step 4: Subtract the product obtained in Step 3 from the original numerator (6x^2 + 35x + 24). The subtraction is done term by term:
(6x^2 + 35x + 24) - (6x^2 + 30x) = 5x + 24.
Step 5: Bring down the next term from the original numerator, which is 5x, and write it next to the result obtained in Step 2.
Step 6: Repeat Steps 2-5 with the new expression (5x + 24) as the numerator.
Step 7: Divide the first term of the new numerator (5x) by the first term of the denominator (x). The result is 5.
Step 8: Multiply the entire denominator (x+5) by the result from Step 7 (5). The product is 5(x+5) = 5x + 25.
Step 9: Subtract the product obtained in Step 8 from the new numerator (5x + 24). The subtraction is done term by term:
(5x + 24) - (5x + 25) = -1.
Step 10: The quotient is the sum of the results from Steps 2 and 7: 6x + 5.
Step 11: The remainder is the result obtained in Step 9: -1.
So, the quotient is 6x + 5 and the remainder is -1.