Question

perform the indicated operation of each function.
$f(x)=(x^4 + 5)$ $g(x)=x^2$ $h(x)=(2x^2 + x - 9)$
①
$f(x)\bullet g(x) - h(x)$

Explanation:

Step1: Multiply \( f(x) \) and \( g(x) \)

We have \( f(x) = x^4 + 5 \) and \( g(x) = x^2 \). Using the distributive property (multiplication of polynomials), we get:
\( f(x) \cdot g(x)=(x^4 + 5)\cdot x^2=x^4\cdot x^2+5\cdot x^2=x^6 + 5x^2 \)

Step2: Subtract \( h(x) \) from the result

We know \( h(x)=2x^2 + x - 9 \). So we subtract \( h(x) \) from \( x^6 + 5x^2 \):
\( (x^6 + 5x^2)-(2x^2 + x - 9)=x^6+5x^2 - 2x^2 - x + 9 \)

Step3: Combine like terms

Combine the \( x^2 \) terms: \( 5x^2-2x^2 = 3x^2 \). So the final expression is \( x^6+3x^2 - x + 9 \)

Answer:

\( x^6 + 3x^2 - x + 9 \)