Question

find the remainder when 4x^3-3x^2+4x-2+4x+2 divide (a)x-1 and(b) x2​

Answer 1

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

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1 Answer

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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.

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Answer 2

Step-by-step explanation:

the answer of a) is 9

and of b) is 0 if 8/x is taken in quotient