Question

1. If 8x⁴ - 8x² + 7 is divided by 2x + 1, the remainder is :-
(a) 11/2 (b) 13/2 (c)15/2 (d)17/2

2. If (x + 1) is a factor of the polynomial p(x) = 2x² + kx, then k = ?
(a) -3 (b) 4 (c) 2 (d) 3​

Answer 1

Answer:

1. (a) 11/2

2.(c) 2

Step-by-step explanation:

1. According to Remainder Theorem, if a polynomial f(x) is divided by ( x - a), then f(a) will be the remainder.

f(x) = 8x⁴ - 8x2 + 7 and a = -1/2

f(-1/2) = 8(-1/2)⁴ - 8(-1/2)2 + 7

= 8 x (1/16) - 8 x (1/4) + 7

= 1/2 - 2 + 7

= 1/2 + 5

= 11/2

2. Since x+1 is the factor

Remainder = 0

∴kx−2x=0

∴kx=2x

∴k=2