As above, let $$f(x) = 3\cdot\frac{x^4+x^3+x^2+1}{x^2+x-2} .$$Give a polynomial $g(x)$ so that $f(x) + g(x)$ has a horizontal asymptote of $y=0$ as $x$ approaches positive infinity.

Hello,

Step-by-step explanation:

Explanation:

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We need p(x) need to be a degree 2 polynomial so the numerator of the second fraction is degree 4. Our goal is to cancel the terms of the first fraction's numerator that are of degree 2 or higher.

So let p(x)=ax^2+bx+c.

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Plug in our p:

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Take a break to multiply the factors of our second fraction's numerator.

Multiply:

=

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=

Let's go back to the problem:

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Let's distribute that 3:

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Next we have . Based on previous statement this forces .

Next we have . With and , this gives .

So which equals .

Lastly, .

This makes .

This implies or simplified

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

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to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.