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:

$p(\frac{3}{4})=2\cdot(\frac{3}{4})^2+9\cdot\frac{3}{4}-9$

Remember that the power of a fraction meets the following:

$(\frac{a}{b})^n=\frac{a^n}{b^n}$

Then we have:

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

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

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

Then the answer is -9/8.