Question

Which number could replace x to make a true statement 2/3 x/8 7/8

Answer 1

Explanation:

Remainder when p(x) is divided by (x+2) is -29

Explanation:

p(x) = x^{3} - 2x^{2} + 8x + kx3−2x2+8x+k

When p(x) is divided by (x-2), remainder is 19.

p(x - 2 = 0) gives the remainder when p(x) is divided by (x-2)

x - 2 = 0

x = 2

p(x-2=0) = p(2) = 2^{3} - 2(2^{2}) + 8(2) + k23−2(22)+8(2)+k = 19

8 - 8 + 16 + k = 19

k = 3

p(x) = x^{3} - 2x^{2} + 8x + 3x3−2x2+8x+3

p(x + 2 = 0) gives the remainder when p(x) is divided by (x+2)

x + 2 = 0

x = -2

p(x+2=0) = p(-2) = (-2)^{3} - 2((-2)^{2}) + 8(-2) + 3(−2)3−2((−2)2)+8(−2)+3

p(-2) = - 8 - 8 - 16 + 3 = -29

Remainder when p(x) is divided by (x+2) is -29