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Q.

Find the value of m so that 2x−1 be a factor of 8X4+4x3-16x2+10x+m


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a

- 1

b

2

c

- 2

d

0 

answer is C.

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Detailed Solution

Concept: Utilize the Remainder Theorem, which asserts that when a polynomial, g(x) , is divided by a linear polynomial, (x-a) , the remainder, g(a) , is obtained. The remainder is the portion of the polynomial that is left over after the division. Only when the polynomial is divided by a linear polynomial is this theorem applicable. A polynomial is an expression made up of variables and coefficients with addition, multiplication, subtraction, and exponent operations. A linear polynomial is typically written as f(x) =ax+b, where b is the constant term.
Here, the dividend to which the number is to be divided is 8X4+4x3−16x2+10x+m, and the divisor by which the number is to be divided to obtain the value of m is 2x1.
Now compare the divisor, a linear polynomial, with 0; this gives us
2x-1=0
2x=1
x=12
Thus, we deduce that when a polynomial of the form 8X4+4x3-16x2+10x+m is divided by the linear polynomial x=12, the remainder is given by the expression g(12) in terms of m.
g(x) =8X4+4x3−16x2+10x+m
=8×116+4×18−16×14+10×12+m
=12+12−4+5+m=1−4+5+m
=2+m
Considering that 2x-1 is a factor of 8X4+4x3−16x2+10x+m, we may equal g(x) =0.
Thus, we obtain g(x) =0
2+m=0
m=-2.
Hence, the correct answer is 3) - 2
 ExamType: CBSE
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