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05/07/2021 11:01 am
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Find the remainder when x3 + 3x2 + 3x + 1 is divided by
(i) x + 1
(ii) x − 1/2
(iii) x
(iv) x + π
(v) 5 + 2x
1 Answer
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05/07/2021 11:05 am
(i) x + 1
x + 1 = 0
⇒ x = −1
∴ Remainder:
p(−1) = (−1)3+3(−1)2 + 3(−1)+1
= −1 + 3 − 3 + 1
= 0
(ii) x−1/2
x-1/2 = 0
⇒ x = 1/2
∴ Remainder:
p(1/2) = (1/2)3 + 3(1/2)2 + 3(1/2) + 1
= (1/8) + (3/4)+(3/2)+1
= 27/8
(iii) x
x = 0
∴Remainder:
p(0) = (0)3 + 3(0)2 + 3(0)+1
= 1
(iv) x+π
x + π = 0
⇒ x = −π
∴ Remainder:
p(0) = (−π)3 + 3(−π)2 + 3(−π) + 1
= −π3+3π2−3π+1
(v) 5+2x
5 + 2x = 0
⇒ 2x = −5
⇒ x = -5/2
∴ Remainder:
(-5/2)3+ 3(-5/2)2 + 3(-5/2) + 1
= (-125/8) + (75/4) - (15/2) + 1
= -27/8