# Common Core: High School - Algebra : Different Forms of Simple Rational Expressions: CCSS.Math.Content.HSA-APR.D.6

## Example Questions

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### Example Question #1 : Different Forms Of Simple Rational Expressions: Ccss.Math.Content.Hsa Apr.D.6

Write the following polynomial quotient in the form

Explanation:

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the  term down.

Now we multiply the zero by the term we just put down, and place it under the  term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the  term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first  numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

### Example Question #1 : Different Forms Of Simple Rational Expressions: Ccss.Math.Content.Hsa Apr.D.6

Write the following polynomial quotient in the form

Explanation:

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the  term down.

Now we multiply the zero by the term we just put down, and place it under the  term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the  term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first  numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

### Example Question #1 : Different Forms Of Simple Rational Expressions: Ccss.Math.Content.Hsa Apr.D.6

Write the following polynomial quotient in the form

Explanation:

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the  term down.

Now we multiply the zero by the term we just put down, and place it under the  term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the  term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first  numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

### Example Question #1 : Different Forms Of Simple Rational Expressions: Ccss.Math.Content.Hsa Apr.D.6

Write the following polynomial quotient in the form

Explanation:

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the  term down.

Now we multiply the zero by the term we just put down, and place it under the  term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the  term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first  numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

### Example Question #5 : Different Forms Of Simple Rational Expressions: Ccss.Math.Content.Hsa Apr.D.6

Write the following polynomial quotient in the form

Explanation:

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the  term down.

Now we multiply the zero by the term we just put down, and place it under the  term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the  term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first  numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

### Example Question #6 : Different Forms Of Simple Rational Expressions: Ccss.Math.Content.Hsa Apr.D.6

Write the following polynomial quotient in the form

Explanation:

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the  term down.

Now we multiply the zero by the term we just put down, and place it under the  term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the  term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first  numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

### Example Question #7 : Different Forms Of Simple Rational Expressions: Ccss.Math.Content.Hsa Apr.D.6

Write the following polynomial quotient in the form

Explanation:

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the  term down.

Now we multiply the zero by the term we just put down, and place it under the  term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the  term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first  numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

### Example Question #8 : Different Forms Of Simple Rational Expressions: Ccss.Math.Content.Hsa Apr.D.6

Write the following polynomial quotient in the form

Explanation:

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the  term down.

Now we multiply the zero by the term we just put down, and place it under the  term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the  term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first  numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

### Example Question #9 : Different Forms Of Simple Rational Expressions: Ccss.Math.Content.Hsa Apr.D.6

Write the following polynomial quotient in the form

Explanation:

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the  term down.

Now we multiply the zero by the term we just put down, and place it under the  term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the  term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first  numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

### Example Question #10 : Different Forms Of Simple Rational Expressions: Ccss.Math.Content.Hsa Apr.D.6

Write the following polynomial quotient in the form

Explanation:

In order to solve this problem, we need to perform synthetic division.

We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

The first step is to bring the coefficient of the  term down.

Now we multiply the zero by the term we just put down, and place it under the  term coefficient.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the  term.

Now we add the column up to get

Now we multiply the number we got by the zero, and place it under the constant term.

Now we add the column up to get

Now we need to write it out in the form of

is the quotient, which is the first  numbers from the synthetic division.

is the remainder, which is the last number in the synthetic division.

is the divisor, which is what we originally divided by.

Now we put this all together to get.

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