Question

Find the value of m so that 2x - 1 be a factor of 8x4 + 4x3 - 16x2 + 10x + m.

Answer 1

See the attachment it will help you

Answer 2

Given,

The main equation is = 8x⁴+4x³-16x²+10x+m

The factor of the main equation is = (2x-1)

To find,

The correct value of the "m".

Solution,

We can easily solve this mathematical problem by using normal algebraic methods. Rest of the procedures are given below.

Let,

p(x) = 8x⁴+4x³-16x²+10x+m

And,

g(x) = 2x-1

Now, we need to calculate the value of "x".

As, g(x) = 2x-1

So, 2x-1 = 0

2x = 1

x = ½

We have to keep in mind that the calculated value of "x" will surely satisfy the main equation.

And, g(x) is the factor of p(x), so the final value of p(x) will be also zero.

So,by putting the values, we get that,

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

½ + ½ - 4 + 5 + m = 0

1+1+m = 0

2+m = 0

m = -2

[This value of "m" will make the (2x-1) a factor of the main equation.]

Hence, the value of "m" will be -2