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3 years ago

8x2 − 5 + 7x4 − 9x − x5

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

8 0

Answer:

$=-\left(x-1\right)\left(x^4-6x^3-6x^2-14x-5\right)$

Step-by-step explanation:

Factor out comon Term -1

$=-\left(x^5-7x^4-8x^2+9x+5\right)$

Factor $x^5-7x^4-8x^2+9x+5:\quad \left(x-1\right)\left(x^4-6x^3-6x^2-14x-5\right)$

$x^5-7x^4-8x^2+9x+5$

Use the rational root theorem

$a_0=5,\:\quad a_n=1$

The dividers of $a_{0}$ : 1, 5, The dividers of $a_n$ : 1

Therefore, check the following rational numbers: ± $\frac{1,\:5}{1}$

$\frac{1}{1}$ is a root of the expression, so factor out $x-1$

$=\left(x-1\right)\frac{x^5-7x^4-8x^2+9x+5}{x-1}$

$\frac{x^5-7x^4-8x^2+9x+5}{x-1}=x^4-6x^3-6x^2-14x-5$

$=x^4-6x^3-6x^2-14x-5$

$=-\left(x-1\right)\left(x^4-6x^3-6x^2-14x-5\right)$

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4 years ago

Read 2 more answers

1)Convert the following binary numbwers into decimal number(only a,b,c,f,i)<br>

kozerog [31]

Answer:

a) 3₁₀

b) 6₁₀

c) 7₁₀

f) 19₁₀

i) 181₁₀

Step-by-step explanation:

<u>Binary to Decimal Conversion (Positional Notation Method)</u>

Multiply each digit by the base (2) raised to the power dependent upon the position of that digit in the binary number.
Sum all the values obtained for each digit.
Express the number as a decimal number by placing subscript 10 after it.

For a binary number with 'n' digits:

The right-most digit is multiplied by 2⁰
The left-most digit is multiplied by $\sf 2^{n-1}$

For example, to convert the binary number 111001₂ into a decimal:

$\begin{array}{ c c c c c c}1 & 1 & 1 & 0 & 0 & 1\\\downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^0\\\end{array}$

Multiply each digit by the base (2) raised to the power as indicated above and sum them:

$=(1 \times 2^5)+(1 \times 2^4)+(1 \times 2^3)+(0 \times 2^2)+(0 \times 2^1)+(1 \times 2^0)$

$= 32+16+8+0+0+1$

$= 57$

Finally, express as a decimal number ⇒ 111001₂ = 57₁₀

<u>Question (a)</u>

$\begin{aligned}\implies 11_2 & = (1 \times 2^1)+(1 \times 2^0)\\& = 2+1\\& = 3\end{aligned}$

Therefore, 11₂ = 3₁₀

<u>Question (b)</u>

$\begin{aligned}\implies 110_2 & = (1 \times 2^2)+(1 \times 2^1)+(0 \times 2^0)\\& = 4+2+0\\& = 6\end{aligned}$

Therefore, 110₂ = 6₁₀

<u>Question (c)</u>

$\begin{aligned}\implies 111_2 & = (1 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =4+2+1\\& = 7\end{aligned}$

Therefore, 111₂ = 7₁₀

<u>Question (f)</u>

$\begin{aligned}\implies 10011_2 & =(1 \times 2^4)+(0 \times 2^3)+ (0 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =16+0+0+2+1\\& = 19\end{aligned}$

Therefore, 10011₂ = 19₁₀

<u>Question (i)</u>

$\phantom{)))}10110101_2 \\\\=(1 \times 2^7)+(0 \times 2^6)+(1 \times 2^5)+(1 \times 2^4)+(0 \times 2^3)+ (1 \times 2^2) +(0 \times 2^1)+(1 \times 2^0)\\\\=128+0+32+16+0+4+0+1\\\\= 181$

Therefore, 10110101₂ = 181₁₀

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2 years ago

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