Factor the high-degree polynomial expression 7x^2+ 42x + 63 = 0.
Find x
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.
To factor the polynomial expression 7x^2 + 42x + 63 = 0, we can start by looking for common factors among the coefficients. In this case, all coefficients (7, 42, 63) have a common factor of 7. Factoring out 7, we get:
7(x^2 + 6x + 9) = 0
Next, we need to factor the quadratic trinomial x^2 + 6x + 9. We can do this by finding two numbers that multiply to give 9 and add up to 6, since the leading coefficient is 1. In this case, the numbers are 3 and 3.
Therefore, the factored form of the expression is:
7(x + 3)(x + 3) = 0
Simplifying further, this can be written as:
7(x + 3)^2 = 0
To find the values of x, we set each factor equal to zero and solve for x:
x + 3 = 0
Subtracting 3 from both sides:
x = -3
Hence, the value of x is -3.
To factor the high-degree polynomial expression 7x^2 + 42x + 63 = 0, we can use the factoring technique.
First, we need to look for common factors among the coefficients of the polynomial. In this case, all the coefficients are divisible by 7, so we can factor it out:
7(x^2 + 6x + 9) = 0
Next, we need to factor the quadratic expression inside the parentheses. We're looking for two binomials that multiply together to give us the quadratic expression. Since the coefficient of the x^2 term is 1, the quadratic can be factored as:
(x + 3)(x + 3) = 0
Now, we have:
7(x + 3)(x + 3) = 0
To find the values of x, we set each factor equal to zero and solve for x:
x + 3 = 0
x = -3
Therefore, the solution to the equation 7x^2 + 42x + 63 = 0 is x = -3.