anonymous
  • anonymous
Need some help on this equation. Use synthetic substitution to find f(3) = 2x^4 - 3x^2 -x +2 When I use synthetic substitution I got 81, which I'm not sure is right. Aren't the synthetic substitution of an equation and direct supposed to be the same?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amistre64
  • amistre64
whats your setup?
amistre64
  • amistre64
the remainder of a synthetic is equal to the direct results ...
amistre64
  • amistre64
remember to zero in the x^3 thats missing vvv 2x^4 - 3x^2 -x +2 2x^4 + 0x^3 - 3x^2 -x +2 0 6 18 -45 and so on 3 | 2 6 -15 -46

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
I did f(3) = 2x^4 - 3x^2 - x + 2 2 -3 -1 + 2 3 _____________6_____9___27______________ 2 3 8 29 = 87?
amistre64
  • amistre64
is my setup readable? i know it differs from the usual textbook setup ..
anonymous
  • anonymous
I'm a bit confused by it - what did you get for your answer?
amistre64
  • amistre64
i see i got a stray negative ....
amistre64
  • amistre64
2x^4 + 0x^3 - 3x^2 -x +2 0 6 18 45 ------------------------------- 3 | 2 6 15 44 the setup should be recognizable, the only thing I have done differently is to retain the variables (they make good reminders), and move the multiplier down to the bottom to relate it to multiplying bottom row values ...
anonymous
  • anonymous
Ah okay, would you continue that set up with multiplying 44 by 3?
amistre64
  • amistre64
yep, and the final would be the +2 tacked onto it :)
anonymous
  • anonymous
So 134 was your answer? That's what I got for my direct substitution so that must be the answer.
anonymous
  • anonymous
Not sure what's going wrong with my synthetic substitution LOL
amistre64
  • amistre64
i see that you forgot to zero out the x^3 term ... synthetic division is very picky about having ALL the coefficients in order.
amistre64
  • amistre64
no room added for 0x^3 f(3) = 2x^4 -3x^2 - x + 2 2 -3 -1 + 2 3 _____________6_____9___27______________ 2 3 8 29 = 87?
anonymous
  • anonymous
So where did the 0x^3 come in exactly? f(3) = 2x^4 - 3x^2 -x +2 Where is it?
amistre64
  • amistre64
do you recall the property, that anything multiplied by 0 is equal to 0? ; and that adding 0 to anything seems rather pointless?
anonymous
  • anonymous
Yes!
amistre64
  • amistre64
a polynomial is defined as:\[P_n(x)=c_ox^n+c_1x^{n-1}+c_2x^{n-2}+...+c_{n-1}~x+c_n\] ALL of the powers of x have to be present, even if one of the "c" values is 0
amistre64
  • amistre64
\[2x^4 - 3x^2 -x +2 ~~\to~~2x^4\color{red}{+0x^3} - 3x^2 -x +2 \]
amistre64
  • amistre64
now the right side contains all the powers of x from 4 to 0
anonymous
  • anonymous
OH OKAY! For example if I have an equation 7x^3 + 5x ^1 + 2, I have to add in 0x^2 inbetween the 2?
anonymous
  • anonymous
*two
amistre64
  • amistre64
count down from 3 to 0, and compare 3 2 1 0 7x^3 + 5x^1 + 2 since there is not x^2 term, its been zeroed out and simplified; put it back in 3 2 1 0 7x^3 + 0x^2 + 5x^1 + 2
anonymous
  • anonymous
Thank you so much! I understand!
amistre64
  • amistre64
spose we had: 2x^5-3x^2+1 :) we are missing the ^4 and ^3 and ^1 parts, add them back in
amistre64
  • amistre64
good luck
anonymous
  • anonymous
2x^5 +0x^4+0x^3-3x^2 +0x^1 + 1 ? lol thanks

Looking for something else?

Not the answer you are looking for? Search for more explanations.