Divide
(x^6-13x^3+42)/(x^3-7)
Please show me how to work the problem
Long division
Answer x^3 -6
do you have an Ti - 84? that will work it for you in a faster and reasonable manner.
To divide the given polynomial expression, (x^6-13x^3+42) by (x^3-7), follow these steps:
Step 1: Write the polynomial expression in descending order of powers of x.
(x^6-13x^3+42) ÷ (x^3-7)
Step 2: Divide the first term of the numerator by the first term of the denominator.
x^6 ÷ x^3 = x^(6-3) = x^3
Step 3: Multiply the result obtained in Step 2 by the full denominator and subtract it from the numerator.
(x^6-13x^3+42) - (x^3-7) * x^3 = x^6 - 13x^3 + 42 - x^6 + 7x^3 = -6x^3 + 42
Step 4: Repeat Steps 2 and 3 with the new numerator obtained in Step 3.
-6x^3 ÷ x^3 = -6
Step 5: Multiply the result obtained in Step 4 by the full denominator and subtract it from the new numerator.
-6x^3 + 42 - (x^3-7) * -6 = -6x^3 + 42 + 6x^3 - 42 = 0
Step 6: The remainder (0 in this case) becomes the divisor in the next step. Since the remainder is 0, the process ends here.
Step 7: Write the final quotient obtained from all the divisions.
Quotient = x^3 - 6
Therefore, the division of (x^6-13x^3+42) by (x^3-7) is equal to x^3 - 6.