Factor the high-degree polynomial expression 7x2+42x+63=0

Question

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:

\[ \boxed{-3} \]