Question

If p(x) = 2x^2 + 9x – 9, find p(3/4)(Type an integer or fraction.)

Answer 1

So we have the following polynomial:

`p(x)=2x^2+9x-9`

And we need to find p(3/4). We just need to replace x with 3/4:

`p((3)/(4))=2\cdot((3)/(4))^2+9\cdot(3)/(4)-9`

Remember that the power of a fraction meets the following:

`((a)/(b))^n=(a^n)/(b^n)`

Then we have:

`\begin{gathered} p((3)/(4))=2\cdot((3)/(4))^2+9\cdot(3)/(4)-9=2\cdot(9)/(16)+(27)/(4)-9 \\ p((3)/(4))=(18)/(16)+(27)/(4)-9 \end{gathered}`

And we can rewrite 27/4 by multiplying and dividing it by 4 and we can multiply and divide 9 by 16:

`\begin{gathered} p((3)/(4))=(18)/(16)+(27)/(4)\cdot(4)/(4)-9\cdot(16)/(16)=(18)/(16)+(108)/(16)-(144)/(16)=(18+108-144)/(16) \\ p((3)/(4))=-(18)/(16)=-(9)/(8) \end{gathered}`

Then the answer is -9/8.