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

Question

Find x

Answer 1

The given polynomial expression is 7x^2 + 42x + 63 = 0.

To factor this expression, we can divide each term by the greatest common factor, which in this case is 7.

Dividing each term by 7, we have:

(x^2 + 6x + 9) = 0.

Now, we can try to factor the quadratic expression (x^2 + 6x + 9) using the product-sum method.

Since the coefficient of the x^2 term is 1, we look for two numbers whose product is 9 and whose sum is 6.

The numbers are 3 and 3, as 3 * 3 = 9 and 3 + 3 = 6.

So, we can factor the quadratic expression as:

(x + 3)(x + 3) = 0.

This can also be written as:

(x + 3)^2 = 0.

To solve for x from this equation, set the expression inside the parentheses equal to zero:

x + 3 = 0.

Subtracting 3 from both sides of the equation, we get:

x = -3.

Therefore, the solution to the polynomial equation 7x^2 + 42x + 63 = 0 is x = -3.