How do you long divide #(8a^2 - 30a + 7) div (2a - 78)#?

Question

Elias Ackerman · Accepted Answer

I tried this:

Have a look:

Cora Alexander · Answer

undefined To long divide $ (8a^2 - 30a + 7) \div (2a - 78) $, you follow the steps of long division similar to dividing numbers.

1. Divide the first term of the dividend by the first term of the divisor.
2. Multiply the divisor by the result obtained in step 1, and write the result under the dividend.
3. Subtract the result obtained in step 2 from the dividend.
4. Bring down the next term of the dividend.
5. Repeat steps 1-4 until all terms of the dividend have been accounted for.

Following these steps:

1. Divide $8a^2$ by $2a$, which gives $4a$.
2. Multiply $2a - 78$ by $4a$, resulting in $8a^2 - 312a$.
3. Subtract $8a^2 - 312a$ from $8a^2 - 30a$, which gives $282a$.
4. Bring down the next term, which is $7$.
5. Divide $282a$ by $2a$, giving $141$.
6. Multiply $2a - 78$ by $141$, resulting in $282a - 11058$.
7. Subtract $282a - 11058$ from $282a + 7$, giving $11065$.

Thus, the quotient is $4a + 141$ with a remainder of $11065$.