Question

factor the high- degree polynomial expression of 7x^2+42x +63=0 and then solve for the value of x x=

Answer 1

First, we can factor the polynomial expression \(7x^2 + 42x + 63 = 0\).

1. **Factor out the greatest common factor:**
The coefficients \(7\), \(42\), and \(63\) have a common factor of \(7\). So, we can factor out \(7\):
\[
7(x^2 + 6x + 9) = 0
\]

2. **Factor the quadratic expression \(x^2 + 6x + 9\):**
The expression can be factored as follows:
\[
x^2 + 6x + 9 = (x + 3)(x + 3) = (x + 3)^2
\]

3. **Combine the factored terms:**
Therefore, we can write the equation as:
\[
7(x + 3)^2 = 0
\]

4. **Set the factors equal to zero:**
Since \(7\) is not equal to zero, we can focus on:
\[
(x + 3)^2 = 0
\]

5. **Solve for \(x\):**
Taking the square root on both sides:
\[
x + 3 = 0
\]
Thus, solving for \(x\), we get:
\[
x = -3
\]

Therefore, the solution for the value of \(x\) is:
\[
\boxed{-3}
\]