5

Use synthetic division and the factor theorem to determine whether x ~ 4 is a factor of f(x). f(x) =4x3_ 19x2 16x 16Complete the first row of the synthetic division...

Question

Use synthetic division and the factor theorem to determine whether x ~ 4 is a factor of f(x). f(x) =4x3_ 19x2 16x 16Complete the first row of the synthetic division table

Use synthetic division and the factor theorem to determine whether x ~ 4 is a factor of f(x). f(x) =4x3_ 19x2 16x 16 Complete the first row of the synthetic division table



Answers

Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first. $$5 x^{4}+16 x^{3}-15 x^{2}+8 x+16 ; x+4$$

This problem asks us to use the factor theorem to see if X minus four is a factor of four X squared plus two X plus 54. And we can do this using synthetic division, So X minus four is a factor of this. To see if it is a factor. We've synthetic division. If it has a remainder of zero, then we'd say Yes, it's a factor if it has any other. Remainder is not a factor. So let's run this synthetic division four times four gives me 16. 2 plus 16 is 18, 4 times 18 gives me 40 plus 32. So that's 72. Add those up and you get 112 116. And that 116 not our Sorry, it's 1 26 1 26 is the remainder. So we would say that that's That's your remainder. So we would say that X minus four is not a factor of that China meal

So in this problem we are asked to find all of the zeros here and to do that. I'm first going to use the rational root beer. Um to divide my last value 16 by my leading coefficient here, in front of the ice of the third, which is 16. And then I'm on the list, all the possible factors that go into 16 which would be plus or minus one plus or minus to plus or minus four Plus or -8 and plus or -16. So these are all the possible rational numbers that go into this function here. Now, sometimes you're going to have to plug these in um and see if you end up with zero quite a bit to determine which one to divide by. I know that this divides by positive too. So I'm gonna go ahead and kind of skip ahead and divide this function by positive too. So I'm gonna go ahead and my first rope, but a leading coefficients, I'm gonna put a placeholder for X squared mm. And I'm dividing by positive too. Bring down my one. Multiply add multiply here. That gives me negative eight. Multiply negative 16 at that gives me zero. So that leaves me with X squared plus two. X minus eight. And I want to see if I can factor this quadratic. So multiplies to negative eight and adds to to that would be positive for and negative two. Yeah. Which means my other two zeros would be negative for two. And then since I had to twice here, I would right next to that multiplicity of two. Yeah. And those would be my three zeros in this cubic.

Okay, so here we're considering the polynomial F of x equal to x Q plus two, X squared plus three and x minus one. Okay, so um for any polynomial F of x equal um fx we know that x minus K is a factor of the polynomial if it only F f of K is equal to zero. So to see whether x minus one is a factor of X squared plus two, X squared, um X cubed plus two X. Crypto three. Well by the factor theorem x minus one will be a factor F F of one is equal to zero. So we can use some studies division here. Um I actually I mean the biggest of division, I mean we can if this is a guessing not really part of this video but um exploring dots, if you never heard of it is amazing thing. And um dividing polynomial was exploring not is so so cool. But gets back to basically what since the division is. So here, I mean again is putting um the coefficient of a polynomial. And we use some tape division here and we see that F. Of one. Well, is that equal to six? So therefore the remainder, The remainder is sex and not zero. So therefore we can say that X -1. Um is not a factor, it's not a factor um of two X cubed plus two X squared plus three. Mhm.

We want to know of X Plus four is the factor of this polynomial. Now we need to list all of the turns because there's no extra. The fifth it's gonna be is euro exit if it power my 16 x to the fourth, and because there's no exit 1/3 B zero x of 1/3 the next word and because there's no access in the zero X minus 16 now, experts for years if I could sterile, excessively negative force your divide by native pouring him a list of all of the factors, including the zeros now at the factor. And if once you divide in and your remainder is zero, then X plus four is a factor of this polynomial, So you bring down the one negative for tons. One is negative for zero plus negative floors. Negative four Negative for time thinking afford is positive. 16. Negative 16 plus 16 in so, well, negative. Four times zero is zero 000 The multiple negative. Four times zero is zero, adding up one negative four tons. One is negative four and then you added up, so we'll get negative for negative four time. Think before is going to be positive. 16 and yet it's gonna be zero because there's gonna be no remainders. X plus four is a factor. So now because we know we started with extra the six power you need to use one power last. So be extra. The fifth minus four extra form. There's no ice or the third no X to the second power. But we do have an axe. We have minus four. And don't forget the other factor of X plus four.


Similar Solved Questions

5 answers
Use potaesfolln Number W M 3 reaction_ Pb(Nos) li how many decimal that you have grams Pblz of lead(ll} 2KNO V iodide , Ik 'alltbe other Hl 37.1 9 ofQ
Use potaesfolln Number W M 3 reaction_ Pb(Nos) li how many decimal that you have grams Pblz of lead(ll} 2KNO V iodide , Ik 'alltbe other Hl 37.1 9 of Q...
5 answers
Suppose that ! of woik needeu Stielcm Sprino Krom natura length 28 cm length 45 CIn . How muon woik needud stretch the sannaom 37 cm? (Round vour ariswcr (wo dearnal places )(b) Hom fut bevond natural lenejth Wa lotce 0l 15 Kr thue spuq stretched? (Round yaui HMAnat deornal place )
Suppose that ! of woik needeu Stielcm Sprino Krom natura length 28 cm length 45 CIn . How muon woik needud stretch the sannaom 37 cm? (Round vour ariswcr (wo dearnal places ) (b) Hom fut bevond natural lenejth Wa lotce 0l 15 Kr thue spuq stretched? (Round yaui HMAnat deornal place )...
5 answers
Study the free body diagram below and choose the statement that best describes the dynamics of the situation:Fw = IONFt= 2N~F4=8N10 NThe net force acting is 26 Nb) The net horizontal force is 10 NThe net force acting is 6 N,The net force acting is 30 N
Study the free body diagram below and choose the statement that best describes the dynamics of the situation: Fw = ION Ft= 2N ~F4=8N 10 N The net force acting is 26 N b) The net horizontal force is 10 N The net force acting is 6 N, The net force acting is 30 N...
5 answers
Do Homework: section 7.2 Score: 0 of 1 pt2 of 6 (4 complete)7.23 Nam Due; Show that the function y = f(x) is a solution of Ihe accompanying differential equation. Last Curr v-iJea xy'tw= e* AttelFind Xy' Xy and xy' +xy fory = XJaatOKTXTnis qui Terms 0
Do Homework: section 7.2 Score: 0 of 1 pt 2 of 6 (4 complete) 7.23 Nam Due; Show that the function y = f(x) is a solution of Ihe accompanying differential equation. Last Curr v-iJea xy'tw= e* Attel Find Xy' Xy and xy' +xy fory = XJaat OK TX Tnis qui Terms 0...
5 answers
X2 _ 3 10. (a) f(x) = x2 + 1(b) f(x) = %x+2
x2 _ 3 10. (a) f(x) = x2 + 1 (b) f(x) = %x+2...
5 answers
For Constitutional Isomers_ the two compounds Name drawn; your pdf decide file as: Koul Stereo 3 Identical, Enantlomers_ YourLastName DiastereomersOH
For Constitutional Isomers_ the two compounds Name drawn; your pdf decide file as: Koul Stereo 3 Identical, Enantlomers_ YourLastName Diastereomers OH...
5 answers
1 2 1 2 $ where _ 'R= {(r,y):0 s*51, 1 '@
1 2 1 2 $ where _ 'R= {(r,y):0 s*51, 1 '@...
5 answers
Grinding wheel ne rom unlform sollld dlsk Taois Mass 5tan om restang accelerates mntformi Wncem {a) How long does the Khee reach its fina operating speeo 130 rev{min?Jcdonconstanc torqueTnactne Mor erens Onetne 4neeiknow the changevelccit and the acceleration Youcenainiy find the tme Can Yov detemlne the (angular) acceleration?(b) Through how many revolutions does tum Ghilelerating?
grinding wheel ne rom unlform sollld dlsk Taois Mass 5tan om restang accelerates mntformi Wncem {a) How long does the Khee reach its fina operating speeo 130 rev{min? Jcdon constanc torque Tnactne Mor erens Onetne 4neei know the change velccit and the acceleration You cenainiy find the tme Can Yov d...
5 answers
* Solrc for Xl ) Vsin3 Lap lecs trasfornX +12 K + 40 X3 sin5€X(o) = 0Rt)eo
* Solrc for Xl ) Vsin3 Lap lecs trasforn X +12 K + 40 X 3 sin5€ X(o) = 0 Rt)eo...
5 answers
Int Vhe (Inat anoxint ot mnonoy In an account 54,800) 1 deposited at 8 % interest cornpomdud weckly nd Iwe motley I Ielt lor 6 yvurs_Tho [lual .uolirieRourd answet t0 2 decImat plee
Int Vhe (Inat anoxint ot mnonoy In an account 54,800) 1 deposited at 8 % interest cornpomdud weckly nd Iwe motley I Ielt lor 6 yvurs_ Tho [lual .uolirie Rourd answet t0 2 decImat plee...
5 answers
3x2 x-2Let f (x)(A) Find the critical number(s) of f . Verify vour solution steps using the definition of critical point;(B) Find the intervals where f is increasing decreasing: Verify your solution steps using the Increasing/Decreasing Test:(C) Investigate whether f has local maximum and minimum value(s). Draw table using the results from parts A) and B) that guide you in this investigation.
3x2 x-2 Let f (x) (A) Find the critical number(s) of f . Verify vour solution steps using the definition of critical point; (B) Find the intervals where f is increasing decreasing: Verify your solution steps using the Increasing/Decreasing Test: (C) Investigate whether f has local maximum and minim...
1 answers
Find $B A^{-1}$. In Exercises $32-34,$ find $C A^{-1}$ $$B=\left[\begin{array}{ll}8 & -2 \\ 3 & 4\end{array}\right]$$ $$C=\left[\begin{array}{rrr}5 & -1 & 0 \\ 2 & -2 & 1 \\ -3 & 0 & 4\end{array}\right]$$ $$A=\left[\begin{array}{rrr} 1 & -1 & 1 \\ 0 & -2 & 1 \\ -2 & -3 & 0 \end{array}\right]$$
Find $B A^{-1}$. In Exercises $32-34,$ find $C A^{-1}$ $$B=\left[\begin{array}{ll}8 & -2 \\ 3 & 4\end{array}\right]$$ $$C=\left[\begin{array}{rrr}5 & -1 & 0 \\ 2 & -2 & 1 \\ -3 & 0 & 4\end{array}\right]$$ $$A=\left[\begin{array}{rrr} 1 & -1 & 1 \\ 0 & -2 &...
1 answers
(II) What voltage is needed to produce electron wavelengths of 0.20 $\mathrm{nm}$ ? (Assume that the electrons are nonrelativistic.)
(II) What voltage is needed to produce electron wavelengths of 0.20 $\mathrm{nm}$ ? (Assume that the electrons are nonrelativistic.)...
1 answers
Use the guidelines of this section to sketch the curve. $$y=x \sqrt{5-x}$$
Use the guidelines of this section to sketch the curve. $$y=x \sqrt{5-x}$$...
5 answers
No Heavy IsotopeSample 18392kvntMass Spectrum[ 1m/z
No Heavy Isotope Sample 18392kvnt Mass Spectrum [ 1 m/z...
5 answers
A planet is orbiting the Sun in an orbit that is nearly circular with an average radius of 1.4 X 1013 m: Assuming that the planet is in uniform circular motion, what is its the centripetal acceleration, in mls?, in its orbit around the Sun? Take the period of the planet around the sun as 1.8 earth-years. Give your answer in three decimal places:
A planet is orbiting the Sun in an orbit that is nearly circular with an average radius of 1.4 X 1013 m: Assuming that the planet is in uniform circular motion, what is its the centripetal acceleration, in mls?, in its orbit around the Sun? Take the period of the planet around the sun as 1.8 earth-y...
5 answers
A metal has work-function (WF) of 1.151eV. What is the kinetic energy of the ejected electron; in units ofeV, if the metal is exposed to radiation of wavelength 384.7 nm?
A metal has work-function (WF) of 1.151eV. What is the kinetic energy of the ejected electron; in units ofeV, if the metal is exposed to radiation of wavelength 384.7 nm?...

-- 0.019142--