Question

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

Answer 1

To factor the polynomial expression \(7x^2 + 42x + 63 = 0\), we can start by factoring out the greatest common factor (GCF):

1. Identify the GCF of the coefficients (7, 42, and 63). The GCF is 7.
2. Factor out 7:

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

3. Now, we can focus on factoring the quadratic \(x^2 + 6x + 9\). This trinomial can be factored as:

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

4. Substitute this back into the equation:

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

5. Now, divide both sides by 7:

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

6. Take the square root of both sides:

\[
x + 3 = 0
\]

7. Finally, solve for \(x\):

\[
x = -3
\]

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

\[
\boxed{-3}
\]