Find a polynomial function f of least degree having the graph sho...

Question

Find a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.)

Accepted Answer

Or the graph given below, find the polynomial function F of minimal degree. You notice here we have a polynomial with three zeros and a Y intercept of 20. No. So possible answers also all have degree three, which means this will be a polynomial of degree three. Now to solve this, let's first find all of our zeros of this function. You notice we have X equals negative five, X equals one and X equals four. We can turn these into factors by moving our numbers to the other side. Get X plus five, X minus one and X minus four. We can then formulate a polynomial by taking F of X equals a constant multiplier a multiplied by all of our zeros X plus five, X minus one, X minus four. Not to find our polynomial. We need to find a and then multiply everything together. We can find a, using R Y intercept. We have a 0.0 20 which we can with two 24 F FX and zero for X equals a multiplied by zero plus five, multiplied by zero minus one and multiplied by zero minus four, you get 20 equals a multiplied by five, 81 and negative four, you will then get 20 equals a multiplied by 20. Finally giving us a equals one. We now have an equation F of X equals X plus five multiplied by X minus one multiplied by X minus four. Let's go ahead and multiply everything together. Now to get our equation, we'll leave X plus five first and work on X minus one multiplied by X minus four. We first take X multiplied by X to get X squared X multiplied by negative four to get negative four, X negative one multiplied by X to get negative X and neither one multiplied by negative four to get positive four, we get X plus five multiplied by X squared minus five X plus four. Now multi further, we will get our first X here or X plus five multiplied by X squared to get X to the third X multiplied by negative five X to get negative five X squared X multiplied by four to get four X and then five multiply to X squared to get five X squared, five multiplied by negative five X to get negative 25 X and five multiplied by four to get 20. We can simplify, we notice we have a negative five X squared and a positive five X squared which should both go away. We will bring down our X to the third combined are four X and negative 25 X to get negative 21 X and finally bring down our 20 we can't simplify any farther. So our function F of X corresponds to answer A OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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Find a polynomial function f of least degree having the graph shown. (Hint: See the NOTE following Example 4.)

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