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) .

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) .
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Solution

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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 \(\boxed{69}\).

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