Question

Find the value of m if 2x-1 is a factor of 8x4+4x^3-16x^2+10x+m.​

Answer 1

Answer:

-2

Step-by-step explanation:

Given polynomial p(x): 8x⁴ + 4x³ - 16x² + 10x + m

Given divisor g(x): 2x - 1

If 2x - 1 = 0, x = ½

It is given that p(x)/g(x) leaves no remainder.

That means p(½) = 0

8(½)⁴ + 4(½)³ - 16(½)² + 10(½) + m = 0

8(1/16) + 4(⅛) - 16(¼) + 10(½) + m = 0

½ + ½ - 4 + 5 + m = 0

1 - 4 + 5 = -m

m = -2

Answer 2

Step-by-step explanation:

Solution

let

p(x) =8x^(4)+4x^(3)-16x^(2)+10x+m

<br> Since , 2x-1 is a factor of p (x) then put

p((1)/(2))=0

<br>

therefore 8((1)/(2))^(4)+4((1)/(2))^(3)-16((1)/(2))^(2)+10((1)/(2))+m=0

<br>

implies 8xx(1)/(16)+4xx(1)/(8) -16xx(1)/(4) +10((1)/(2))+m=0

<br>

implies (1)/(2) +(1)/(2)-4+5+m=0

<br>

implies 1+1+m=0

<br>

therefore m=-2

<br> hence , the value of m is -2.