polynomial

algebra

exponents
in Algebra 1 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Try different values of x to observe the behaviour of p(x).

x=0: p(0)=0, because 40 mod (x+4)=40 mod 4=0.

x=1: p(1)=k+24, because 40 mod 5=0. If k+24=-28, then k=-52.

x=-1: p(-1)=5-k, because 40 mod 3=1. If 5-k=-28, then k=33.

x=2: p(2)=8k+74, because 40 mod 6=4. If 8k+74=-28, then k=-102/8=-51/4.

These give different values for k, so there is no single solution for k. However, if the question is supposed to read: p(x)=(kx^3+15x^2+9x-40) mod (x+4)=-28, the situation is quite different.

Using synthetic division, we can work out the remainder: -64k+164=-28. The modulo function only requires the remainder, which we know is -28; therefore 64k=192 and k=3.

Details of division:

-4 | k......15..........9...........-40

......k.....-4k 16k-60 -64k+204

......k 15-4k 16k-51 -64k+164 (=-28)

 

by Top Rated User (775k points)

Related questions

1 answer
2 answers
asked Oct 22, 2014 in Algebra 2 Answers by jerrod | 172 views
1 answer
asked Sep 25, 2013 in Algebra 2 Answers by jlee | 134 views
1 answer
asked Sep 7, 2013 in Algebra 2 Answers by anonymous | 174 views
1 answer
0 answers
asked Jun 1, 2013 in Algebra 1 Answers by anonymous | 302 views
0 answers
asked Apr 18, 2013 in Algebra 1 Answers by anonymous | 118 views
1 answer
1 answer
asked Mar 7, 2013 in Algebra 1 Answers by anonymous | 209 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,262 questions
90,527 answers
2,148 comments
82,432 users