Give a polynomial division that has a quotient of x+5 and a remainder of -2

sibuzwaW
2021-02-11
Answered

Give a polynomial division that has a quotient of x+5 and a remainder of -2

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Daphne Broadhurst

Answered 2021-02-12
Author has **109** answers

Step 1

Solution :

The polynomial division for the following quotient of x+5 and the remainder of -2 will be

${x}^{3}+{x}^{2}+x+1$

Step 2

$\frac{x+5}{{x}^{2}}){x}^{3}+{x}^{2}+x+1{x}^{2}+x+1$ where the remainder will be -2

Solution :

The polynomial division for the following quotient of x+5 and the remainder of -2 will be

Step 2

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Proof of ${e}^{\mathrm{ln}(x)\mathrm{ln}(2)}$, which natural logarithm do I bring down?

I'm currently stumped with the proof for the following problem:

$F(x)={2}^{\mathrm{ln}(x)}$

$\Rightarrow F(x)=y$

$y={2}^{\mathrm{ln}(x)}$

$\mathrm{ln}(y)=\mathrm{ln}({2}^{\mathrm{ln}(x)})$

$\mathrm{ln}(y)=\mathrm{ln}(x)\cdot \mathrm{ln}(2)$

$y={e}^{\mathrm{ln}(x)\cdot \mathrm{ln}(2)}$

Now, how do I know which natural logarithm to bring down? What ensures that my answer must be ${2}^{\mathrm{ln}(x)}$ instead of ${x}^{\mathrm{ln}(2)}$?

Thanks! :)

I'm currently stumped with the proof for the following problem:

$F(x)={2}^{\mathrm{ln}(x)}$

$\Rightarrow F(x)=y$

$y={2}^{\mathrm{ln}(x)}$

$\mathrm{ln}(y)=\mathrm{ln}({2}^{\mathrm{ln}(x)})$

$\mathrm{ln}(y)=\mathrm{ln}(x)\cdot \mathrm{ln}(2)$

$y={e}^{\mathrm{ln}(x)\cdot \mathrm{ln}(2)}$

Now, how do I know which natural logarithm to bring down? What ensures that my answer must be ${2}^{\mathrm{ln}(x)}$ instead of ${x}^{\mathrm{ln}(2)}$?

Thanks! :)

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