Question

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

Answer 1

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

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

2. **Factor out the GCF**:
\[
7(x^2 + 6x + 9) = 0
\]

3. **Factor the quadratic**: Next, we can factor the quadratic expression \(x^2 + 6x + 9\).
This can be factored as:
\[
(x + 3)(x + 3) \quad \text{or} \quad (x + 3)^2
\]

4. **Write the complete factorization**:
\[
7(x + 3)^2 = 0
\]

5. **Set the factors to zero**: Now we can solve for \(x\) by setting each factor equal to zero:
\[
7 = 0 \quad (\text{no solution here}),
\]
and
\[
(x + 3)^2 = 0
\]

6. **Solve for \(x\)**:
\[
x + 3 = 0
\]
\[
x = -3
\]

Therefore, the solution to the equation \(7x^2 + 42x + 63 = 0\) is:
\[
\boxed{-3}
\]