How do you find the quotient of #(a^2+4a+3)div(a-1)# using long division?

Question

Hazel Anglin · Accepted Answer

You do it just like you divide numbers.

Eva Abramson · Answer

undefined To find the quotient of (a^2+4a+3) divided by (a-1) using long division, follow these steps:

1. Divide the first term of the dividend (a^2) by the first term of the divisor (a). The result is a, which becomes the first term of the quotient.

2. Multiply the divisor (a-1) by the first term of the quotient (a). The result is a^2-a.

3. Subtract the product obtained in step 2 from the dividend (a^2+4a+3). This gives you a remainder of 5a+3.

4. Bring down the next term of the dividend (-5a) and divide it by the first term of the divisor (a). The result is -5, which becomes the second term of the quotient.

5. Multiply the divisor (a-1) by the second term of the quotient (-5). The result is -5a+5.

6. Subtract the product obtained in step 5 from the remainder (5a+3). This gives you a new remainder of -2.

7. Bring down the last term of the dividend (2) and divide it by the first term of the divisor (a). The result is 2, which becomes the third term of the quotient.

8. Multiply the divisor (a-1) by the third term of the quotient (2). The result is 2a-2.

9. Subtract the product obtained in step 8 from the remainder (-2). This gives you a final remainder of 0.

10. The quotient is the sum of the terms obtained in steps 1, 4, and 7, which is a-5+2, or simply a-3.

Julia Adams · Answer

undefined To find the quotient of $\frac{{a^2 + 4a + 3}}{{a - 1}}$ using long division:

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 product below the dividend.
3. Subtract the product obtained in step 2 from the first polynomial.
4. Bring down the next term of the dividend and repeat steps 1-3 until the division is complete or until the degree of the remainder is less than the degree of the divisor.

Let's go through the steps:

Step 1: $a^2$ divided by $a$ equals $a$.

Step 2: Multiply $a - 1$ by $a$ to get $a^2 - a$, write it below $a^2 + 4a + 3$.

Step 3: Subtract $a^2 - a$ from $a^2 + 4a + 3$ to get $5a + 3$.

Step 4: Bring down the next term, which is $4a$.

Step 5: $5a$ divided by $a$ equals $5$.

Step 6: Multiply $a - 1$ by $5$ to get $5a - 5$, write it below $5a + 3$.

Step 7: Subtract $5a - 5$ from $5a + 3$ to get $8$.

The quotient is $a + 5$ and the remainder is $8$.