Question

Factor the high-degree polynomial expression 7x^2+42x+63=0 then solve for x

Answer 1

Let's start by factoring the polynomial expression \( 7x^2 + 42x + 63 = 0 \).

First, we can factor out the greatest common factor (GCF), which is 7:

\[
7(x^2 + 6x + 9) = 0
\]

Now, we can focus on the quadratic expression \( x^2 + 6x + 9 \). We will factor this expression. We can rewrite it as:

\[
x^2 + 6x + 9 = (x + 3)(x + 3) = (x + 3)^2
\]

So the equation now looks like this:

\[
7(x + 3)^2 = 0
\]

Next, we can set this equation to zero:

\[
(x + 3)^2 = 0
\]

To solve for \( x \), we take the square root of both sides:

\[
x + 3 = 0
\]

Subtracting 3 from both sides gives us:

\[
x = -3
\]

Thus, the solution to the equation \( 7x^2 + 42x + 63 = 0 \) is:

\[
\boxed{-3}
\]