Final answer:
The question involves using Polynomial Long Division to divide (6x⁴−28x²−9x+10) by (x+2). In algebra, when dividing exponentials, subtract the exponents. The process is iterative until the remainder is of lower degree than the divisor or there is no remainder.
Step-by-step explanation:
To divide the polynomial (6x⁴−28x²−9x+10) by (x+2), we use Polynomial Long Division. This is similar to long division with numbers. Let's start by setting up the division:
Step 1: Divide the first term of the numerator, 6x⁴, by the first term of the denominator, x, which gives us 6x³. Write this above the division bar.
Step 2: Multiply the entire divisor (x+2) by 6x³ and subtract the result from the original polynomial. Simplify.
Step 3: Repeat the process with the new polynomial you have after simplification. Divide the new leading term by x, multiply the divisor by the result, and subtract again.
Step 4: Continue this process until you reach a remainder that is of a lower degree than the divisor or until there is no remainder.
In Division Techniques in Algebra, dealing with exponents when dividing is also important. When dividing two exponentials, subtract the exponents -- this is a basic rule of exponents that applies in polynomial division as well.
Examples of Division of Exponentials: To divide 10⁶ by 10³, we subtract the exponents to get 10³.
Finally, to check if the solution is plausible, Eliminate terms wherever possible to simplify the algebra and always check the answer to see if it's reasonable.