Divide: (20b^(3)+17b^(2)+18b+43)÷(4b+5)
Given that 5 does not divide 43, will will have a remainder. Doing the long division, we get
5b^2 - 2b + 7 + 8/(4b+5)
Thank you.
Hope that helped. It's hard to show the work of long division when the browser does its own formatting of the text.
To divide the polynomial (20b^(3) + 17b^(2) + 18b + 43) by (4b + 5), you can use long division. Here's how:
Step 1: Start by dividing the highest degree term of the dividend (20b^(3)) by the highest degree term of the divisor (4b). The result of this step will be the first term of the quotient.
5b^(2)
Step 2: Multiply the entire divisor, (4b + 5), by the first term of the quotient, 5b^(2).
5b^(2) * (4b + 5) = 20b^(3) + 25b^(2)
Step 3: Subtract the product obtained in the previous step from the dividend.
(20b^(3) + 17b^(2) + 18b + 43) - (20b^(3) + 25b^(2)) = -8b^(2) + 18b + 43
Step 4: Bring down the next term from the dividend. In this case, it is 18b.
-8b^(2) + 18b + 43
Step 5: Repeat steps 1-4 with the new dividend.
Divide (-8b^(2)) by (4b) = -2b
Multiply (-2b) by (4b + 5) = -8b^(2) - 10b
Subtract the obtained product from the new dividend:
(-8b^(2) + 18b + 43) - (-8b^(2) - 10b) = 28b + 43
Step 6: Bring down the last term from the dividend. In this case, it is 43.
28b + 43
Step 7: Repeat steps 1-4 with the new dividend.
Divide (28b) by (4b) = 7
Multiply (7) by (4b + 5) = 28b + 35
Subtract the obtained product from the new dividend:
(28b + 43) - (28b + 35) = 8
Since the new dividend, 8, has a lower degree than the divisor (4b + 5), the division process is complete.
Therefore, the quotient of (20b^(3) + 17b^(2) + 18b + 43) divided by (4b + 5) is:
5b^(2) - 2b + 7, with a remainder of 8.