can somme one please help me. i need answers for 1.divide (x2-10x+30)divided by (x-5) 2.divide (x3-20x+16)divided by (x-4) 3. divide (-4x3+35x+25)divided by(-2x-5) 4.divide (-7x+x2+15)divided by(-3+x)
Of course, I can help you with these division problems step-by-step. Let's go through them one by one:
1. To divide (x^2 - 10x + 30) by (x - 5), start by dividing the first term of the numerator (x^2) by the denominator (x). This gives you x as the quotient. Multiply x by (x - 5), which gives you x * (x - 5) = x^2 - 5x.
2. Subtract this result (x^2 - 5x) from the original numerator (x^2 - 10x + 30). The result is (-10x + 30) - (-5x) = -10x + 5x + 30 = -5x + 30.
3. Now divide (-5x + 30) by (x - 5). Start by dividing the first term (-5x) by the denominator (x), which gives you -5 as the quotient. Multiply -5 by (x - 5) to get -5 * (x - 5) = -5x + 25.
4. Subtract this result (-5x + 25) from the original numerator (-5x + 30). The result is (30) - (25) = 5.
So, the solution to (x^2 - 10x + 30) / (x - 5) is x - 5.
Now, let's move on to the next problem:
2. To divide (x^3 - 20x + 16) by (x - 4), follow the same steps as above.
First, divide the first term of the numerator (x^3) by the denominator (x). This gives you x^2 as the quotient. Multiply x^2 by (x - 4), which gives you x^2 * (x - 4) = x^3 - 4x^2.
Now subtract this result (x^3 - 4x^2) from the original numerator (x^3 - 20x + 16). The result is (-20x + 16) - (-4x^2) = -20x + 4x^2 + 16.
Now, divide (-20x + 4x^2 + 16) by (x - 4). Divide the first term (-20x) by the denominator (x), which gives you -20 as the quotient. Multiply -20 by (x - 4) to get -20 * (x - 4) = -20x + 80.
Subtract this result (-20x + 80) from the original numerator (-20x + 4x^2 + 16). The result is (4x^2 + 16) - (80) = 4x^2 - 64.
So, the solution to (x^3 - 20x + 16) / (x - 4) is x^2 - 20 - 4 / (x - 4).
Moving on to the third problem:
3. To divide (-4x^3 + 35x + 25) by (-2x - 5), follow the same steps as above.
First, divide the first term of the numerator (-4x^3) by the denominator (-2x). This gives you 2x^2 as the quotient. Multiply 2x^2 by (-2x - 5), which gives you 2x^2 * (-2x - 5) = -4x^3 - 10x^2.
Subtract this result (-4x^3 - 10x^2) from the original numerator (-4x^3 + 35x + 25). The result is (35x + 25) - (-10x^2) = 35x + 10x^2 + 25.
Now, divide (35x + 10x^2 + 25) by (-2x - 5). Divide the first term (35x) by the denominator (-2x), which gives you -17.5 as the quotient. Multiply -17.5 by (-2x - 5) to get -17.5 * (-2x - 5) = 35x + 87.5.
Subtract this result (35x + 87.5) from the original numerator (35x + 10x^2 + 25). The result is (10x^2 + 25) - (87.5) = 10x^2 - 62.5.
So, the solution to (-4x^3 + 35x + 25) / (-2x - 5) is 2x^2 -17.5 + (-2x - 5) / (-2x - 5).
Finally, let's address the fourth problem:
4. To divide (-7x + x^2 + 15) by (-3 + x), follow the same steps as before.
First, divide the first term of the numerator (x^2) by the denominator (x), which gives you x as the quotient. Multiply x by (-3 + x), which gives you x * (-3 + x) = -3x + x^2.
Subtract this result (-3x + x^2) from the original numerator (-7x + x^2 + 15). The result is (15 - 7x) - (-3x + x^2) = 15 - 7x + 3x - x^2 = -x^2 - 4x + 15.
Now, divide (-x^2 - 4x + 15) by (-3 + x). Divide the first term (-x^2) by the denominator (x), which gives you -x as the quotient. Multiply -x by (-3 + x) to get -x * (-3 + x) = 3x - x^2.
Subtract this result (3x - x^2) from the original numerator (-x^2 - 4x + 15). The result is (-4x + 15) - (3x - x^2) = 15 - 4x - 3x + x^2 = x^2 - 7x + 15.
So, the solution to (-7x + x^2 + 15) / (-3 + x) is -x + 15 + x^2 - 7x / (-3 + x).
I hope this helps!
Of course, I'd be happy to help you with those division problems! To divide polynomials, we can use polynomial long division. Here are the step-by-step solutions to each problem:
1. Divide (x^2 - 10x + 30) by (x - 5):
Step 1: Write the dividend (x^2 - 10x + 30) in descending order of powers: x^2 - 10x + 30
Step 2: Divide the first term of the dividend (x^2) by the divisor (x), and write the result on the top line: x
Step 3: Multiply the divisor (x - 5) by the quotient obtained from the previous step (x). Write the result under the first two terms of the dividend: x(x - 5) = x^2 - 5x
Step 4: Subtract the product obtained in the previous step (x^2 - 5x) from the dividend (x^2 - 10x + 30): (x^2 - 10x + 30) - (x^2 - 5x) = -5x + 30
Step 5: Bring down the next term of the dividend (-5x) and repeat the process.
Step 6: Divide the first term of the new dividend (-5x) by the divisor (x), and write the result on the top line: -5
Step 7: Multiply the divisor (x - 5) by the new quotient obtained (-5). Write the result under the new dividend term: -5(x - 5) = -5x + 25
Step 8: Subtract the product obtained in the previous step (-5x + 25) from the new dividend (-5x + 30): (-5x + 30) - (-5x + 25) = 5
The resulting quotient is (x - 5) with a remainder of 5.
2. Divide (x^3 - 20x + 16) by (x - 4):
For this problem, you can follow the same steps as explained above for polynomial long division.
3. Divide (-4x^3 + 35x + 25) by (-2x - 5):
Again, follow the same steps of polynomial long division.
4. Divide (-7x + x^2 + 15) by (-3 + x):
Once again, you can use polynomial long division to solve this problem.
I recommend performing the calculations step by step neatly to avoid any mistakes.
for all the details of long division, you can verify your results by entering your polynomials at
http://calc101.com/webMathematica/long-divide.jsp