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P(x) =x5 + 2x3 +1
Answers
Step-by-step explanation:
When divided by x - 1, the polynomial P(x) = x5 + 2x3 +Ax + B, where A and B are constants, the remainder is equal to 2. When P(x) is divided by x + 3, the remainder is equal -314. Can you help me Find A and B?
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4 Answers

Elaine Dawe, BMath, Mathematics & Computer Science, University of Waterloo (1985)
Answered February 28, 2019 · Author has 3.1K answers and 1.8M answer views
P(x)/(x−1)P(x)/(x−1) gives remainder of 2⟹P(1)=22⟹P(1)=2
15+2(1)3+A(1)+B=215+2(1)3+A(1)+B=2
3+A+B=23+A+B=2
A+B=−1A+B=−1
P(x)/(x+3)P(x)/(x+3) gives remainder of −314⟹P(−3)=−314−314⟹P(−3)=−314
(−3)5+2(−3)3+A(−3)+B=−314(−3)5+2(−3)3+A(−3)+B=−314
−297−3A+B=−314−297−3A+B=−314
3A−B=173A−B=17
Add both equations:
4A=164A=16
A=4A=4
Plug into first equation:
4+B=−14+B=−1