Questions: 7x^7+28x^6+28x^5

Transcript text: $7 x^{7}+28 x^{6}+28 x^{5}$

Solution

Step 1: Identify the Polynomial

We start with the polynomial $7x^7 + 28x^6 + 28x^5$.

Step 2: Find the Greatest Common Factor

The greatest common factor (GCF) of the terms $7x^7$, $28x^6$, and $28x^5$ is $7x^5$.

Step 3: Factor Out the GCF

We factor out $7x^5$ from the polynomial: \[ 7x^7 + 28x^6 + 28x^5 = 7x^5(x^2 + 4x + 4) \]

Step 4: Factor the Remaining Polynomial

Next, we factor the quadratic $x^2 + 4x + 4$: \[ x^2 + 4x + 4 = (x + 2)^2 \]

Step 5: Write the Complete Factored Form

Combining the factors, we have: \[ 7x^7 + 28x^6 + 28x^5 = 7x^5(x + 2)^2 \]

$\boxed{7x^5(x + 2)^2}$

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