Common Core: High School - Algebra : Arithmetic with Polynomials & Rational Expressions

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 #141 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when  is divided by 

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 constant term.

Now we add the column together to get.

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

Example Question #142 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when  is divided by 

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 constant term.

Now we add the column together to get.

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

Example Question #143 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when  is divided by x

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 constant term.

Now we add the column together to get.

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

Example Question #144 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when  is divided by 

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 constant term.

Now we add the column together to get.

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

Example Question #1 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the -intercept(s) of the function?

Possible Answers:

Correct answer:

Explanation:

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a  value equal to zero.

One technique that can be used is factorization. In general form,

where,

 and  are factors of  and when added together results in .

For the given function,

 

the coefficients are,

therefore the factors of  that have a sum of  are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

Screen shot 2016 03 08 at 11.06.54 am

The graph crosses the -axis at -2 and 3, thus verifying the results found by factorization. 

Example Question #212 : High School: Algebra

What are the -intercept(s) of the function?

Possible Answers:

Correct answer:

Explanation:

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a  value equal to zero.

One technique that can be used is factorization. In general form,

where,

 and  are factors of  and when added together results in .

For the given function,

 

the coefficients are,

therefore the factors of  that have a sum of  are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

Screen shot 2016 03 08 at 12.13.08 pm

The graph crosses the -axis at 3 and 4, thus verifying the results found by factorization. 

Example Question #3 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the -intercept(s) of the function?

Possible Answers:

Correct answer:

Explanation:

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a  value equal to zero.

One technique that can be used is factorization. In general form,

where,

 and  are factors of  and when added together results in .

For the given function,

 

the coefficients are,

therefore the factors of  that have a sum of  are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

Screen shot 2016 03 08 at 12.27.49 pm

The graph crosses the -axis at -3 and -6, thus verifying the results found by factorization. 

Example Question #4 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the -intercept(s) of the function?

Possible Answers:

Correct answer:

Explanation:

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a  value equal to zero.

One technique that can be used is factorization. In general form,

where,

 and  are factors of  and when added together results in .

For the given function,

 

the coefficients are,

therefore the factors of  that have a sum of  are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

Screen shot 2016 03 08 at 12.52.32 pm

The graph crosses the -axis at -4 and 2, thus verifying the results found by factorization. 

Example Question #1 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the -intercept(s) of the function?

Possible Answers:

Correct answer:

Explanation:

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a  value equal to zero.

One technique that can be used is factorization. In general form,

where,

 and  are factors of  and when added together results in .

For the given function,

 

the coefficients are,

therefore the factors of  that have a sum of  are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

Screen shot 2016 03 08 at 1.07.18 pm

The graph crosses the -axis at -1, thus verifying the result found by factorization. 

Example Question #3 : Identify Zeros, Factor And Graph Polynomials: Ccss.Math.Content.Hsa Apr.B.3

What are the -intercept(s) of the function?

Possible Answers:

Correct answer:

Explanation:

To find the -intercept of a function, first recall that the -intercept represents the points where the graph of the function crosses the -axis. In other words where the function has a  value equal to zero.

One technique that can be used is factorization. In general form,

where,

 and  are factors of  and when added together results in .

For the given function,

 

the coefficients are,

therefore the factors of  that have a sum of  are,

Now find the -intercepts of the function by setting each binomial equal to zero and solving for .

To verify, graph the function.

Screen shot 2016 03 08 at 1.27.02 pm

The graph crosses the -axis at -6 and -1, thus verifying the results found by factorization. 

All Common Core: High School - Algebra Resources

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