# Common Core: High School - Algebra : Remainder Theorem: CCSS.Math.Content.HSA-APR.B.2

## Example Questions

### Example Question #1 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when  is divided by

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 constant term.

Now we add the column together to get.

The last number is the remainder, so our final answer is .

### Example Question #2 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when  is divided by

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 constant term.

Now we add the column together to get.

The last number is the remainder, so our final answer is

### Example Question #3 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when  is divided by

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 constant term.

Now we add the column together to get.

The last number is the remainder, so our final answer is

### Example Question #4 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when  is divided by

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 constant term.

Now we add the column together to get.

The last number is the remainder, so our final answer is

### Example Question #5 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when  is divided by

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 \uptext{x} 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 constant term.

Now we add the column together to get.

The last number is the remainder, so our final answer is

### Example Question #6 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when  is divided by

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 \uptext{x} 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 constant term.

Now we add the column together to get.

The last number is the remainder, so our final answer is

### Example Question #7 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when  is divided by

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 \uptext{x} 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 constant term.

Now we add the column together to get.

The last number is the remainder, so our final answer is

### Example Question #8 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when  is divided by

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 constant term.

Now we add the column together to get.

The last number is the remainder, so our final answer is .

### Example Question #9 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when  is divided by

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 constant term.

Now we add the column together to get.

The last number is the remainder, so our final answer is

### Example Question #10 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when  is divided by

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 constant term.

Now we add the column together to get.

The last number is the remainder, so our final answer is