Questions: Factor the following expression completely: 21a^4 + 28a^3 - 7a^2 Submit Question

Solution Steps

The given expression is \(21a^4 + 28a^3 - 7a^2\). First, we identify the greatest common factor (GCF) of the coefficients and the variables.

• The coefficients are 21, 28, and -7. The GCF of these numbers is 7.
• The variable part is \(a^4\), \(a^3\), and \(a^2\). The GCF of these terms is \(a^2\).

Thus, the GCF of the entire expression is \(7a^2\).

We factor out \(7a^2\) from each term in the expression:

\[ 21a^4 + 28a^3 - 7a^2 = 7a^2(3a^2 + 4a - 1) \]

Now, we attempt to factor the quadratic expression \(3a^2 + 4a - 1\). We look for two numbers that multiply to \(3 \times (-1) = -3\) and add to 4. However, there are no such integers, so the quadratic cannot be factored further using integers.

Final Answer