find the remainder when 4x^3-3x^2+4x-2+4x+2 divide (a)x-1 and(b) x2
Answers
If p(x) = 4x3 – 3x2 + 2x – 4 find the remainder when p(x) is divided by :
(i) x – 4 (ii) x + 2 (iii) x + ½
factorization
Please log in or register to answer this question.
1 Answer
0
votes
answered Feb 25, 2019 by muskan15 (-3,443 points)
(i) p(x) = 4x3 – 3x2 + 2x – 4 …(i)
Put x = 4 in equation (i), we get
p(4) = 4(4)3 – 3(4)2 + 2(4) – 4
= 4 × 64 – 3 × 16 + 8 – 4
= 256 – 48 + 8 – 4
= 264 – 52 = 212
Hence, the remainder is 212.
(ii) p(x) = 4x3 – 3x2 + 2x – 4 …(i)
By the remainder theorem the required remainder = p(-2).
Put x = - 2 in equation (i), we get
p(- 2) = 4(- 2)3 – 3(- 2)2 + 2(- 2) – 4
= 4 × (- 8) – 3 × 4 - 4 – 4
= - 32 – 12 – 4 – 4 = - 52
Hence, the remainder is - 52.
(iii) p(x) = 4x3 – 3x2 + 2x – 4 …(i)
By the remainder theorem the required remainder
= p(- ½)
Put x = (-1/2) in equation (i) we get
p(-1/2) = 4(- ½)3 – 3(-1/2)2 + 2(-1/2) - 4
= 4 × (- 1/8) – 3 × ¼ + 2 × (- ½) – 4
= - ½ - ¾ - 1 – 4
= - 2 – 3 – 4 – 16/4 = - 25/4
Hence, the remainder is – 25/4.
Please mark me as brainliest so I can answer more questions like this one.
Step-by-step explanation:
the answer of a) is 9
and of b) is 0 if 8/x is taken in quotient