(24b^3+16b^2+24b+39)/(4b+4)
To simplify the given expression, we can use polynomial long division. Here's how to do it step by step:
Step 1: Write the equation in the correct order. We can rearrange the equation in the form of (dividend)/(divisor).
(24b^3 + 16b^2 + 24b + 39) / (4b + 4)
Step 2: Divide the first term of the dividend by the first term of the divisor. In this case, divide 24b^3 by 4b, which gives us 6b^2.
Step 3: Multiply the divisor by the result obtained in step 2. Multiply (4b + 4) by 6b^2, which gives us 24b^3 + 24b^2.
Step 4: Subtract the product obtained in step 3 from the original dividend. Subtract (24b^3 + 24b^2) from (24b^3 + 16b^2 + 24b + 39):
(24b^3 + 16b^2 + 24b + 39) - (24b^3 + 24b^2)
Simplified result: -8b^2 + 24b + 39
Step 5: Bring down the next term from the original dividend. Bring down the term +24b:
-8b^2 + 24b + 39
Step 6: Repeat steps 2-5 until the degree of the divisor exceeds the degree of the remaining dividend. In this case, the degree of the divisor is 1 (leading term is 4b), and the degree of the remaining dividend is 1 (leading term is 24b).
Step 2: Divide the first term of the remaining dividend by the first term of the divisor. In this case, divide 24b by 4b, which gives us 6.
Step 3: Multiply the divisor by the result obtained in step 2. Multiply (4b + 4) by 6, which gives us 24b + 24.
Step 4: Subtract the product obtained in step 3 from the remaining dividend. Subtract (24b + 24) from (24b + 0):
(24b + 0) - (24b + 24)
Simplified result: -24
Step 5: There is no more term to bring down, so we have our final result, -24.
Therefore, the simplified expression is:
(24b^3 + 16b^2 + 24b + 39) / (4b + 4) = 6b^2 - 8b + 6 - 24 / (4b + 4)