Divide: 20x^2+31x-16/4x-1?

Question

I do not even know where to begin can someone help me?

Answer 1

To begin, you first figure out which operations to perform first:
the rule is:
1. parentheses
2. exponentiation
3. Multiplication and division
4. Addition and subtraction

Let's use parentheses to show the order
20x^2+31x-16/4x-1
20(x^2)+31x-16/4x-1
(20(x^2))+(31x)-((16/4)x)-1
then perform the operations, or simplify, etc.

However, because of the way you phrased your question, you may be implying:
(20x^2+31x-16)/(4x-1)
which sounds more like what a teacher would ask.
remember:
(a+b+c)/d = (a/d) + (b/d) + (c/d)
so separate the left section into its additive parts and prepare to divide each by the right section:
(20x^2) / (4x-1)
+ (31x) / (4x-1)
+ (-16) / (4x-1)

part1 prep:
20x^2 / 4x would be 5x
5x * (4x-1) is 20x^2 - 5x
so to make part 1 easily divisible bring -5x over from part 2:
(20x^2-5x) / (4x-1)
+ (31x + 5x) / (4x-1) ***or*** + (36x) / (4x-1)
+ (-16) / (4x-1)

part2 prep:
36x / 4x would be 9
9 * (4x-1) is 36x - 9
so to make part 2 easily divisible bring -9 over from part 3:
(20x^2-5x) / (4x-1)
+ (36x-9) / (4x-1)
+ (-16+9) / (4x-1) ***or*** +(-7) / (4x-1)

part3 prep:
nothing else left to draw from so not much is possible here

now perform the divisions in each part:
5x
+9
-7/(4x-1)
***or***
5x + 9 - 7 / (4x-1)


In this case, spit the left section into its component part

Answer 2

(20x^2+31x-16)/(4x-1)
= (20x^2-5x + 36x-9 - 16+9)/(4x-1)
= (5x + 9) - 7/(4x-1)
-----------
You can also use long division or synthetic division.

Answer 3

Just use long division and you will get:
5x +9 -7/(4x-1)

Answer 4

i'm not going to give you the answer because this is kinda hard...but i will give you some tricks on how to solve it......mostly, in these types of problems, you must pay attention to the signs because one little mistake on reading the problem, you could get an entirely different answer....Hope i helped and best of luck to you...!!!!