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Use the Remainder Theorem to evaluate P(c) P(x) = x4 + 8x3 Tx - 11_ C = f(-1)...

Question

Use the Remainder Theorem to evaluate P(c) P(x) = x4 + 8x3 Tx - 11_ C = f(-1)

Use the Remainder Theorem to evaluate P(c) P(x) = x4 + 8x3 Tx - 11_ C = f(-1)



Answers

Use the remainder theorem to find $f(c)$. $$f(x)=x^{4}+3 x^{2}-12 ; \quad c=-2$$

So here. FX Eco's too Acts of Powerful Plus Euro Acts of Power three minus X x choir plus four x minus eight So P X year equals two X plus three. Now we can x to the power of three to it, you have extra powerful plus reacts to power of three Oh, mhm. So here we can see that equal to minus reacts to the power of three Okay, minus six x choir plus for ACS minus eight and then the time three extra power to we'll have minus three x to the power of three minus ni act Squire So your house three x choir plus for X minus eight So now it times it by three and see that he has to three x three x power off to last night X, and that one equals two minus five x minus eight So we can say by minus five we'll have minus five x minus 15. The swon gives us seven so we'll see off a minus three equals to the remainder which he goes to seven here and then we can check about it So f minus three equals two. 81. That ISS minus traitor. Powerful minus six times nine. Last four times minus three minus eight. So 81 minus 54. Minus 12. Minus eight. So those one equals two. 27 miners. 20. You can see that it also ecosystem.

Visit Poland but 37 in which B X is given as four X squared plus 12 X plus five and see equal to minus one. So we need to find the value of PC. That is the off minds when using synthetic division Endymion. So we'll be urine Synthetic division. I'm sorry that this is a coefficient of X square. They sick over centre backs. This is constant term. Okay, so let us right. Minus one here individual before foreign to minus one. That is minus four. That is eight minus A that is minus three. So they said the remainder. So we can say that according to demand it to him be off miners when equal toe my industry So this dance Thank you so much.

Here. We have given Botox is acquittal or excess square plus 12 X plus five. And we have even season four to minus on and we need to find bi op. Si So Hey, villa. Bless interdict using method. So you relate. Minus one. And here. Well, well. And five again. This four will be returned here and on multiplying minus on before we got plus off. Minus off on addict. Well, with minus off would be good place off it. And on my depending minus on with a big auto minus off it. Our table is completely therefore on anything with five foot minus eight. We got minus artery, therefore or final answer that is B O minus one. Did his pitches remainder be off minus one is equal to minus off tree.

We're evaluating P off. See using the remainder theorem and synthetic division the remainder Ethereum staged that if p of X is divided by X minus c, the remainder in this case has called a remainder. Our vics is equal to PFC yo or divisor to. In this case, D of X is equal to X minus. C on Dorsey is equal to negative one Teoh x minus c becomes X plus one. So a statement you have x divided by Do you have X is equal to for ex great push 12 eggs plus five over eggs. Close one. We're going to you synthetic division as stated before where the coefficients of the polynomial in the numerator or are written So we have four well on five. Andi he waiting eggs Purcell one on devices to zero we saw for X that gives us negative one. Therefore, to the left off or first row, we have negative one. Or simply we didn't you will have to e quit the device. It is your own solve for X you could have just used or c trying old or the vision we need to add to rose one hair on Dhere bringing our for it onto the third row. We multiply negative one by four, which gives us negative for adding negative for 2 12 results. He knows getting eight multiplying eight by negative one gives us negative eight. Adding negative eight to fire gives us native city therefore or every window is now your duty on door quotient. We get that by multiplying or in numbers by the respective X term. So eight is multiplied by X rays to zero. Four is multiplied by extras too. One, therefore or quotient is equal Jew who are eggs plus eight on or remainder, which is what we're actually concerned. It is equal to negative three. So recall that I said earlier that or remainder is what p. Of sees equal Jew. Therefore, PFC, he's equal to you now. You 23


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