Question

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The questions are in the attachment....... I need the answers to 15 and 16th question....... no spams plz ☺

Answer 1

HEYA !!

15.

p(x) = x^3 - 5x^2 + 4x -3

g(x) = x - 2

x - 2 = 0

x = 2

p(2) = 2^3 - 5×2^2 + 4 × 2 -3

= 8 - 20 +8 - 3

= 16 - 23

= - 7


Here, the remainder is not zero so p(x) is not a multiple of g(x).

16.

p(x) = 2x^3 - 11x^2 - 4x + 5

g(x) = 2x + 1

2x + 1 = 0

2x = -1

x = -1/2

p(-1/2) = 2 × (-1/2)^3 - 11 × (-1/2)^2 - 4 × (-1/2) + 5

= 2 × -1/8 - 11 × 1/4 -4 × -1/2 + 5

= -2/8 - 11/4 + 2 + 5

= 4


Here, the remainder is not equal to zero so g(x) is not a factor of p(x)...