Common Core: High School - Algebra : High School: Algebra

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

Write the following polynomial quotient in the form 

 

Possible Answers:

 

Correct answer:

 

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

Write the following polynomial quotient in the form 

 

Possible Answers:

 

Correct answer:

 

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 

 

Possible Answers:

 

Correct answer:

 

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

Write the following polynomial quotient in the form  

Possible Answers:

Correct answer:

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

Write the following polynomial quotient in the form 

 

Possible Answers:

Correct answer:

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

Write the following polynomial quotient in the form 

 

Possible Answers:

 

Correct answer:

 

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

Write the following polynomial quotient in the form 

 

Possible Answers:

 

Correct answer:

 

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 #391 : High School: Algebra

Simplify:

Possible Answers:


 

Correct answer:

Explanation:

The first step we need to take in order to simplify this expression is to find a common denominator.

We do this by multiplying by a clever form of one to each fraction.


Now we can use FOIL for the numerator and the denominator.


Now we can combine the fractions since they have a common denominator, and put the like terms together.

Example Question #2 : Rational Expressions: Ccss.Math.Content.Hsa Apr.D.7

Simplify: 

Possible Answers:


 

Correct answer:


 

Explanation:

The first step we need to take in order to simplify this expression is to find a common denominator.

We do this by multiplying by a clever form of one to each fraction.


Now we can use FOIL for the numerator and the denominator.


Now we can combine the fractions since they have a common denominator, and put the like terms together.

Example Question #3 : Rational Expressions: Ccss.Math.Content.Hsa Apr.D.7

Simplify: 

Possible Answers:

 

 

Correct answer:

Explanation:

The first step we need to take in order to simplify this expression is to find a common denominator.

We do this by multiplying by a clever form of one to each fraction.

Now we can use FOIL for the numerator and the denominator.

Now we can combine the fractions since they have a common denominator, and put the like terms together.

All Common Core: High School - Algebra Resources

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