consider the following quadratic equation x^(2)+18x+81=0 using the standard form ax^(2)+bx+c=0 of the given quadratic equation factor the left hand side of the equation into two linear factors
To factor the quadratic equation x^2 + 18x + 81 = 0, we need to find two linear factors that, when multiplied, give the quadratic expression.
We can start by looking at the constant term, which is 81. Since it is positive, the factors of 81 will either both be positive or both be negative.
Next, let's look at the coefficient of x, which is 18. We need to find two numbers that multiply to give 81 (the constant term) and add up to give 18 (the coefficient of x).
The factors of 81 are: ±1, ±3, ±9, ±27, and ±81.
Since the coefficient of x is positive (18), we are looking for two numbers that multiply to give a positive product (81) and add up to give a positive sum (18).
After checking different pairs of numbers from the factors of 81, we find that the numbers 9 and 9 meet these conditions: 9 * 9 = 81, and 9 + 9 = 18.
Therefore, we can factor the quadratic equation x^2 + 18x + 81 = 0 as (x + 9)(x + 9) or (x + 9)^2.
So, the left-hand side of the equation can be factored into two linear factors as (x + 9)(x + 9) or (x + 9)^2.