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All Common Core: High School - Algebra Resources

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Flashcards: Remainder Theorem: CCSS.Math.Content.HSA-APR.B.2

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

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Flashcards: Remainder Theorem: CCSS.Math.Content.HSA-APR.B.2

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

Your answer:

Correct answer:

Explanation:

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc} 1 & 9 & 2 & 0 \\ ~ & ~ & ~ & ~ \\ \hline ~ & 9 & ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc} 1 & 9 & 2 & 0 \\ ~ & ~ & 9 & ~ \\ \hline ~ & 9 & ~ & ~ \end{tabular}$

Now we add the column up to get

$\begin{tabular}{ c| ccc} 1 & 9 & 2 & 0 \\ ~ & ~ & 9 & ~ \\ \hline ~ & 9 & 11 & ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc} 1 & 9 & 2 & 0 \\ ~ & ~ & 9 & 11 \\ \hline ~ & 9 & 11 & ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc} 1 & 9 & 2 & 0 \\ ~ & ~ & 9 & 11 \\ \hline ~ & 9 & 11 & 11 \end{tabular}$

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

Flashcards: Remainder Theorem: CCSS.Math.Content.HSA-APR.B.2

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

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Flashcards: Remainder Theorem: CCSS.Math.Content.HSA-APR.B.2

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

Your answer:

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.

$\begin{tabular}{ c| ccc} 9 & 1 & -18 & 3 \\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$
The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc} 9 & 1 & -18 & 3 \\ ~ & ~ & ~ & ~ \\ \hline ~ & 1 & ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.
$\begin{tabular}{ c| ccc} 9 & 1 & -18 & 3 \\ ~ & ~ & 9 & ~ \\ \hline ~ & 1 & ~ & ~ \end{tabular}$
Now we add the column up to get

$\begin{tabular}{ c| ccc} 9 & 1 & -18 & 3 \\ ~ & ~ & 9 & ~ \\ \hline ~ & 1 & -9& ~ \end{tabular}$
Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc} 9 & 1 & -18 & 3 \\ ~ & ~ & 9 & -81 \\ \hline ~ & 1 & -9 & ~ \end{tabular}$
Now we add the column together to get.

$\begin{tabular}{ c| ccc} 9 & 1 & -18 & 3 \\ ~ & ~ & 9 & -81 \\ \hline ~ & 1 & -9 &-78 \end{tabular}$

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

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All Common Core: High School - Algebra Resources

Flashcards: Remainder Theorem: CCSS.Math.Content.HSA-APR.B.2

Flashcards: Remainder Theorem: CCSS.Math.Content.HSA-APR.B.2

Flashcards: Remainder Theorem: CCSS.Math.Content.HSA-APR.B.2

Flashcards: Remainder Theorem: CCSS.Math.Content.HSA-APR.B.2

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