Question

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camilla is designing a platform for an athletic awards ceremony. the areas for two of the three faces of a platform are given. the height of the platform is the gcf of the polynomials representing the given areas. answer parts a through d.a. what are the dimensions of each face of the platform?face a: $\boldsymbol{3x^2 + x}$face b: $\boldsymbol{x^2 + x}$face c:

Explanation:

Step1: Factor Face A's area

Factor $3x^2 + x$ by extracting GCF:
$3x^2 + x = x(3x + 1)$

Step2: Factor Face B's area

Factor $x^2 + x$ by extracting GCF:
$x^2 + x = x(x + 1)$

Step3: Identify shared dimension

The shared factor (height) is $x$. So the other dimensions are $3x+1$ and $x+1$.

Step4: Find Face C's dimensions

Face C area is product of $3x+1$ and $x+1$, so dimensions are $3x+1$ and $x+1$.

Answer:

Face A: $x$ and $3x+1$
Face B: $x$ and $x+1$
Face C: $3x+1$ and $x+1$