Question

H(x)=x-1/2 is a factor of f(x)=2x^4+x^3+x-3/4

Answer 1

True

Explanation:

Answer 2

`\large{\text{Yes.}\ f(x)=x-(1)/(2) \text{is a factor of}\ f(x)=2x^4+x^3+x-(3)/(4).}`

Explanation:

`\text{If}\ (x-a)\ \text{is a factor of}\ p(x),\ \text{then}\ p(a)=0.`

`\text{Thereofre if}\ h(x)=x-(1)/(2)\ \text{is a factor of}\ f(x)=2x^4+x^3+x-(3)/(4),\ \text{then}\ f\left((1)/(2)\right)=0.`

`\text{Substitute:}\\\\f\left((1)/(2)\right)=2\left((1)/(2)\right)^4+\left((1)/(2)\right)^3+(1)/(2)-(3)/(4)=2\left((1)/(16)\right)+(1)/(8)+(1)/(2)-(3)/(4)\\\\=(1)/(8)+(1)/(8)+(1\cdot2)/(2\cdot2)-(3)/(4)=(1+1)/(8)+(2)/(4)-(3)/(4)=(2)/(8)+(2)/(4)-(3)/(4)\\\\=(1)/(4)+(2)/(4)-(3)/(4)=(1+2-3)/(4)=(0)/(4)=0`