Factor the high-degree polynomial expression 7x^2+ 42x + 63 = 0.

Answer 1

To factor the high-degree polynomial expression 7x^2 + 42x + 63 = 0, we begin by finding the greatest common factor (GCF) of the coefficients of the polynomial, which is 7.

Next, we divide each term of the polynomial by the GCF:
7x^2 + 42x + 63 = 7(x^2 + 6x + 9)

Now, we try to factor the quadratic expression inside the parentheses: x^2 + 6x + 9.

The quadratic expression can be factored as (x + 3)(x + 3), since 3 * 3 = 9 and 3 + 3 = 6.

Therefore, 7(x^2 + 6x + 9) = 7(x + 3)(x + 3).

So the factored form of the polynomial expression 7x^2 + 42x + 63 = 0 is 7(x + 3)(x + 3).