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2 years ago

Based on the polynomial remainder theorem, what is the value of the function when x = 3?

Mathematics

2 answers:

matrenka [14]2 years ago

7 0

Answer: 64

Step-by-step explanation:

f(x) = x⁴ + 3x³ - 6x² -12x -8

when x= 3

f(3) = (3)⁴ + 3(3)³ - 6(3)² -12(3) -8

=81 + 3(27) - 6(9)- 12(3) - 8

= 81 + 81 - 54 - 36 - 8

= 64

Therefore, when x= 3 the function becomes; f(3)=64

dsp732 years ago

5 0

Answer:

Step-by-step explanation:

Evaluate x^4 + 3 x^3 - 6 x^2 - 12 x - 8 where x = 3:

x^4 + 3 x^3 - 6 x^2 - 12 x - 8 = 3^4 + 3×3^3 - 6×3^2 - 12×3 - 8

3^3 = 3×3^2:

3^4 + 3×3×3^2 - 6×3^2 - 12×3 - 8

3^2 = 9:

3^4 + 3×3×9 - 6×3^2 - 12×3 - 8

3×9 = 27:

3^4 + 3×27 - 6×3^2 - 12×3 - 8

3^2 = 9:

3^4 + 3×27 - 69 - 12×3 - 8

3^4 = (3^2)^2:

(3^2)^2 + 3×27 - 6×9 - 12×3 - 8

3^2 = 9:

9^2 + 3×27 - 6×9 - 12×3 - 8

9^2 = 81:

81 + 3×27 - 6×9 - 12×3 - 8

3×27 = 81:

81 + 81 - 6×9 - 12×3 - 8

-6×9 = -54:

81 + 81 + -54 - 12×3 - 8

-12×3 = -36:

81 + 81 - 54 + -36 - 8

81 + 81 - 54 - 36 - 8 = (81 + 81) - (54 + 36 + 8):

(81 + 81) - (54 + 36 + 8)

| 8 | 1

+ | 8 | 1

1 | 6 | 2:

162 - (54 + 36 + 8)

| 1 |

| 5 | 4

| 3 | 6

+ | | 8

| 9 | 8:

162 - 98

| | 15 |

| 0 | 5 | 12

| 1 | 6 | 2

- | | 9 | 8

| 0 | 6 | 4:

Answer: 64

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Lesechka [4]

Answer:

$\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}$

________

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Step-by-step explanation:

Given

$21\:\times \:14$

Line up the numbers

$\begin{matrix}\space\space&2&1\\ \times \:&1&4\end{matrix}$

Multiply the top number by the bottom number one digit at a time starting with the ones digit left(from right to left right)

Multiply the top number by the bolded digit of the bottom number

$\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}$

Multiply the bold numbers: 1×4=4

$\frac{\begin{matrix}\space\space&2&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&4\end{matrix}}$

Multiply the bold numbers: 2×4=8

$\frac{\begin{matrix}\space\space&\textbf{2}&1\\ \times \:&1&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&8&4\end{matrix}}$

Multiply the top number by the bolded digit of the bottom number

$\frac{\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&8&4\end{matrix}}$

Multiply the bold numbers: 1×1=1

$\frac{\begin{matrix}\space\space&\space\space&2&\textbf{1}\\ \space\space&\times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&\space\space&8&4\\ \space\space&\space\space&1&\space\space\end{matrix}}$

Multiply the bold numbers: 2×1=2

$\frac{\begin{matrix}\space\space&\space\space&\textbf{2}&1\\ \space\space&\times \:&\textbf{1}&4\end{matrix}}{\begin{matrix}\space\space&\space\space&8&4\\ \space\space&2&1&\space\space\end{matrix}}$

Add the rows to get the answer. For simplicity, fill in trailing zeros.

$\frac{\begin{matrix}\space\space&\space\space&2&1\\ \space\space&\times \:&1&4\end{matrix}}{\begin{matrix}\space\space&0&8&4\\ \space\space&2&1&0\end{matrix}}$

adding portion

$\begin{matrix}\space\space&0&8&4\\ +&2&1&0\end{matrix}$

Add the digits of the right-most column: 4+0=4

$\frac{\begin{matrix}\space\space&0&8&\textbf{4}\\ +&2&1&\textbf{0}\end{matrix}}{\begin{matrix}\space\space&\space\space&\space\space&\textbf{4}\end{matrix}}$

Add the digits of the right-most column: 8+1=9

$\frac{\begin{matrix}\space\space&0&\textbf{8}&4\\ +&2&\textbf{1}&0\end{matrix}}{\begin{matrix}\space\space&\space\space&\textbf{9}&4\end{matrix}}$

Add the digits of the right-most column: 0+2=2

$\frac{\begin{matrix}\space\space&\textbf{0}&8&4\\ +&\textbf{2}&1&0\end{matrix}}{\begin{matrix}\space\space&\textbf{2}&9&4\end{matrix}}$

Therefore,

$\begin{matrix}\space\space&\textbf{2}&\textbf{1}\\ \times \:&1&\textbf{4}\end{matrix}$

________

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6 0

3 years ago

What is the solution set of x2 + 5x - 5 = 0?

Llana [10]

If you're completing the square the answer is in the image.

expression

x^2 + 5x - 5=ax^2+bx+c

a=1, b=5, c=-5, and you can solve it that way.

4 0

3 years ago

Please explain your answer

Ymorist [56]

Answer:

Step-by-step explanation:

11+(-7)^2-9 - original

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60-9 - add both positives 11+49=60

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2 years ago

Evaluate 6 over 3 plus 7 and times 4

jolli1 [7]

Answer:

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Step-by-step explanation:

6^3 +7*4

PEMDAS says exponents first

216 + 7*4

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Now we add and subtract

244

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3 years ago

Read 2 more answers

The fourth term of an Arithmetic Sequence is equal to 3 times the first term, and the seventh term exceeds twice the third term

11Alexandr11 [23.1K]

Answer:

The first term is 3. The common difference is 2.

Step-by-step explanation:

The first term is x.

The common difference is d.

The second term is x + d.

3rd term: x + 2d

4th term: x + 3d

7th term: x + 6d

"The fourth term of an Arithmetic Sequence is equal to 3 times the first term"

x + 3d = 3 * x Eq. 1

"the seventh term exceeds twice the third term by 1"

x + 6d = 2(x + 2d) + 1 Eq. 2

Simplify Eq. 1:

2x = 3d

Simplify Eq. 2:

x + 6d = 2x + 4d + 1

x = 2d - 1

Multiply both sides of the last equation by 2.

2x = 4d - 2

2x = 3d (simplified Eq. 1)

Since 2x = 2x, then the right sides are equal.

3d = 4d - 2

d = 2

2x = 3d

2x = 3(2)

2x = 6

x = 3

Answer: The first term is 3. The common difference is 2.

8 0

2 years ago