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

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

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All Common Core: High School - Algebra Resources

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Example Questions

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

What is the remainder when \displaystyle 9 x^{2} + 2 x is divided by \displaystyle x - 1

Possible Answers:

\displaystyle 2

\displaystyle 12

\displaystyle 11

\displaystyle 3

\displaystyle 1

Correct answer:

\displaystyle 11

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 \displaystyle 11.

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

What is the remainder when \displaystyle x^2- 18 x + 3 is divided by \displaystyle x - 9

Possible Answers:

\displaystyle -87

\displaystyle -16

\displaystyle -25

\displaystyle -78

\displaystyle -54

Correct answer:

\displaystyle -78

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 \displaystyle -78

Example Question #13 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle 19 x^{2} + 4 x - 1 is divided by \displaystyle x + 17

Possible Answers:

\displaystyle 289

\displaystyle 5422

\displaystyle 23

\displaystyle 312

\displaystyle 22

Correct answer:

\displaystyle 5422

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 \displaystyle 5422

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

What is the remainder when \displaystyle - 15 x^{2} + 18 x + 3 is divided by \displaystyle x + 1

Possible Answers:

\displaystyle 3

\displaystyle 4

\displaystyle -30

\displaystyle 1

\displaystyle 6

Correct answer:

\displaystyle -30

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 \displaystyle -30

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

What is the remainder when \displaystyle 19 x^{2} + x + 6 is divided by \displaystyle x + 18

Possible Answers:

\displaystyle 20

\displaystyle 26

\displaystyle 324

\displaystyle 6144

\displaystyle 344

Correct answer:

\displaystyle 6144

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 \displaystyle 6144

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

What is the remainder when \displaystyle - 12 x^{2} - 15 x + 5 is divided by \displaystyle x + 17

Possible Answers:

\displaystyle 289

\displaystyle 262

\displaystyle -27

\displaystyle -3208

\displaystyle -22

Correct answer:

\displaystyle -3208

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 \displaystyle -3208

Example Question #91 : High School: Algebra

What is the remainder when  \displaystyle 18 x^{2} - 15 x - 6 is divided by \displaystyle x + 15

Possible Answers:

\displaystyle 4269

\displaystyle -3

\displaystyle 225

\displaystyle 3

\displaystyle 228

Correct answer:

\displaystyle 4269

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 \displaystyle 4269

Example Question #16 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle - 4 x^{2} - 13 x + 2 is divided by \displaystyle x - 11

Possible Answers:

\displaystyle -15

\displaystyle -17

\displaystyle -625

\displaystyle 121

\displaystyle 104

Correct answer:

\displaystyle -625

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 \displaystyle -625.

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

What is the remainder when \displaystyle - 3 x^{2} + 18 x - 2 is divided by \displaystyle x + 13

Possible Answers:

\displaystyle 15

\displaystyle 169

\displaystyle 13

\displaystyle -743

\displaystyle 184

Correct answer:

\displaystyle -743

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 \displaystyle -743

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

What is the remainder when \displaystyle 17 x^{2} - 19 x + 5 is divided by \displaystyle x - 4

Possible Answers:

\displaystyle -2

\displaystyle 201

\displaystyle 14

\displaystyle 3

\displaystyle 16

Correct answer:

\displaystyle 201

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 \displaystyle 201

All Common Core: High School - Algebra Resources

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