Simplify using long division. (remember to show all your work.) 3. (72-8x^2+4x^3-36x)/(x-3) 4. (8b^3-6)/(2b-1) simplify the expression, if possible. state the excluded values, if any. 5. 10x^2-25X+15^5x-5 6.2w^2-18^w^2+6w+9
try this:
http://calc101.com/webMathematica/long-divide.jsp
To simplify expressions using long division, we will divide the numerator by the denominator term by term. Let's go through the steps for each problem you have provided.
1. Simplify using long division: (72 - 8x^2 + 4x^3 - 36x) / (x - 3)
The first step is to set up the long division problem:
4x^2 + 24x + 72
_____________________
x - 3 | 4x^3 - 8x^2 - 36x + 72
First, divide the highest degree term of the numerator by the highest degree term of the denominator. In this case, divide 4x^3 by x, which gives 4x^2. Write this quotient above the horizontal line.
Next, multiply the entire denominator (x - 3) by the quotient (4x^2) and write the result below the numerator:
4x^2(x - 3) = 4x^3 - 12x^2
Subtract this result from the numerator: (4x^3 - 8x^2 - 36x + 72) - (4x^3 - 12x^2) = 4x^2 - 36x + 72
Now, bring down the next term (-36x) and repeat the process. Divide 4x^2 by x, resulting in 4x. Write this quotient above the horizontal line.
Multiply the denominator (x - 3) by the new quotient (4x): 4x(x - 3) = 4x^2 - 12x
Subtract this result from the previous remainder: (4x^2 - 36x + 72) - (4x^2 - 12x) = -24x + 72
We only have a constant term left (-24x) since there are no terms with lower degrees of x. Bring down the constant term and divide it by x, yielding -24. Write this quotient above the horizontal line.
Multiply the denominator (x - 3) by the new quotient (-24): -24(x - 3) = -24x + 72
Subtract this result from the previous remainder: (-24x + 72) - (-24x + 72) = 0
Since we have obtained a remainder of 0, the division is exact, and the simplified form of the expression is:
4x^2 + 4x - 24
2. Simplify using long division: (8b^3 - 6) / (2b - 1)
Setting up the long division problem:
4b^2 + 2b + 1
_____________________________
2b - 1 | 8b^3 + 0b^2 + 0b - 6
Dividing the highest degree term, 8b^3, by 2b yields 4b^2. Write this quotient above the horizontal line.
Multiply the denominator (2b - 1) by the quotient (4b^2): (2b - 1)(4b^2) = 8b^3 - 4b^2
Subtract this result from the numerator: (8b^3 + 0b^2 + 0b - 6) - (8b^3 - 4b^2) = 4b^2 + 0b - 6
Since the next term (0b) is zero, we don't need to perform any further divisions. The remainder is -6.
Therefore, the simplified form of the expression is:
4b^2 + 2b + 1 - (6 / (2b - 1))
3. Simplify expression: 10x^2 - 25x + 15^5x - 5
This expression seems to have a typo, as it is unclear what the '^5x' part stands for. If you meant to include an exponent for the variable x, please clarify the expression to proceed with the simplification.
4. Simplify expression: 2w^2 - 18^w^2 + 6w + 9
In this expression, we need to clarify what you meant when stating '18^w^2.' Please provide the proper expression with correct formatting for me to assist you further.