Questions: Categorize the expression as a monomial, a binomial, or a trinomial. Then evaluate the polynomial given (x=-3).
(4 x+x^4)
(4 x+x^4) is a (Choose one) .
Transcript text: Categorize the expression as a monomial, a binomial, or a trinomial. Then evaluate the polynomial given $x=-3$.
\[
4 x+x^{4}
\]
$4 x+x^{4}$ is a $\square$ (Choose one) .
Solution
Solution Steps
Step 1: Identify the type of polynomial
The expression \(4x + x^4\) has two terms: \(4x\) and \(x^4\). A polynomial with two terms is called a binomial.
Step 2: Substitute \(x = -3\) into the expression
Replace \(x\) with \(-3\) in the expression:
\[
4(-3) + (-3)^4
\]
Step 3: Simplify the expression
Calculate each term separately:
\[
4(-3) = -12
\]
\[
(-3)^4 = 81
\]
Now, add the results:
\[
-12 + 81 = 69
\]
The expression \(4x + x^4\) is a binomial, and its value at \(x = -3\) is \(69\).
Final Answer
The expression \(4x + x^4\) is a \(\text{binomial}\) and its value at \(x = -3\) is \(\boxed{69}\).