Question

Factor the high-degree polynomial expression 7x2+42x+63=0
and then solve for the value of x
.(1 point)

Answer 1

To factor the polynomial expression \(7x^2 + 42x + 63 = 0\), we can first factor out the greatest common factor (GCF) from the expression.

The GCF of \(7x^2\), \(42x\), and \(63\) is \(7\). Thus, we can factor out \(7\):

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

Next, we need to factor the quadratic expression \(x^2 + 6x + 9\). This quadratic can be factored as follows:

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

Putting it all together, the original expression factors to:

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

To solve for \(x\), we set the factored equation equal to zero:

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

Dividing both sides by \(7\):

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

Taking the square root of both sides:

\[
x + 3 = 0
\]

Subtracting \(3\) from both sides gives:

\[
x = -3
\]

Thus, the solution for \(x\) is:

\[
\boxed{-3}
\]