Question

box 3:
length = $4 + x$
width = $x$
height = $x^2 + 1$

the polynomial that represents the volume of box 3 has a degree of $\boldsymbol{
ule{2cm}{0.15mm}}$.

Explanation:

Step1: Recall volume formula

Volume $V = \text{Length} \times \text{Width} \times \text{Height}$

Step2: Substitute given expressions

$V = (4+x) \times x \times (x^2+1)$

Step3: Identify highest degree terms

The highest degree term from each factor: $x$ (from $4+x$), $x$ (from $x$), $x^2$ (from $x^2+1$)

Step4: Calculate degree of product

Multiply the highest degree terms: $x \times x \times x^2 = x^{1+1+2} = x^4$
The degree of the polynomial is the exponent of this term.

Answer:

4