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 #123 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle - 17 x^{2} + 12 x - 9 is divided by \displaystyle x + 2

Possible Answers:

\displaystyle -92

\displaystyle 4

\displaystyle -5

\displaystyle -1

\displaystyle -14

Correct answer:

\displaystyle -92

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 -101.

Example Question #124 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle - 13 x^{2} + 15 x + 2 is divided by \displaystyle x - 7

Possible Answers:

\displaystyle 51

\displaystyle 4

\displaystyle 2

\displaystyle 49

\displaystyle -532

Correct answer:

\displaystyle -532

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 -530.

Example Question #125 : Arithmetic With Polynomials & Rational Expressions

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

Possible Answers:

\displaystyle 80

\displaystyle 16

\displaystyle 16

\displaystyle 5

Correct answer:

\displaystyle 80

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 85.

Example Question #126 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle 6 x^{2} + 8 x - 7 is divided by \displaystyle x - 19

Possible Answers:

\displaystyle 7

\displaystyle 14

\displaystyle 2318

\displaystyle 375

\displaystyle 361

Correct answer:

\displaystyle 2318

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 2311.

Example Question #121 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle 11 x^{2} + 4 x + 3 is divided by \displaystyle x + 18

Possible Answers:

\displaystyle 15

\displaystyle 339

\displaystyle 324

\displaystyle 3492

\displaystyle 18

Correct answer:

\displaystyle 3492

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 3495.

Example Question #128 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle - 8 x^{2} + 11 x + 1 is divided by \displaystyle x + 15

Possible Answers:

\displaystyle 225

\displaystyle 4

\displaystyle 3

\displaystyle -1965

\displaystyle 228

Correct answer:

\displaystyle -1965

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 -1964.

Example Question #122 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle - 13 x^{2} - 10 x - 10 is divided by \displaystyle x - 18

Possible Answers:

\displaystyle -23

\displaystyle 301

\displaystyle -4392

\displaystyle -33

\displaystyle 324

Correct answer:

\displaystyle -4392

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 -4402.

Example Question #123 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle - 11 x^{2} - 6 x + 7 is divided by \displaystyle x - 12

Possible Answers:

\displaystyle -1656

\displaystyle 127

\displaystyle -10

\displaystyle 144

\displaystyle -17

Correct answer:

\displaystyle -1656

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 -1649.

Example Question #131 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle - 14 x^{2} + 4 x - 2 is divided by \displaystyle x + 18

Possible Answers:

\displaystyle -4608

\displaystyle -10

\displaystyle -12

\displaystyle 314

\displaystyle 324

Correct answer:

\displaystyle -4608

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 -4610.

Example Question #132 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when \displaystyle 4 x^{2} + 2 x + 6 is divided by \displaystyle x + 2

Possible Answers:

\displaystyle 6

\displaystyle 12

\displaystyle 10

\displaystyle 4

\displaystyle 12

Correct answer:

\displaystyle 12

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 18.

All Common Core: High School - Algebra Resources

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