Topic: Math Help Please?
December 12, 2019 / By Cheyenne Question:
Please answer I don't get these questions
x2 + 20x + 99
x2 - 3x - 88
x2 + 11x + 30
x2 + x - 30
Amaria | 3 days ago
These are the type of questions given for practice in factoring. Set the equation equal to 0 and then factor. Each factor produces an answer, so there will be two answers.
Factoring involves finding two expressions that, when multiplied together, gives you the original equation.
For the first equation,
x^2 + 20x + 99 = 0
(x + 11) (x + 9) = 0
x = 11 = 0 x + 9 = 0
x = -11 x = -9
The second equation factors into
(x + 8) (x - 11)
The third equation factors into
(x + 5) (x + 6)
The fourth equation factors into
(x - 5) (x + 6)
As shown in the first example, once you have two factors, set each factor equal to zero and solve for the variable. The reason that there are two answers rather than just one is that you are working with quadratic equations (equations with a term raised to the power of 2). If you thnk about it, it will make no difference whether either of the two answers or both of them are positive or negative, because any number squared is a positive number.
It appears as though this set of problems was designed to have you work out the positive and negative signs to be assigned to the factors, based on the sign you need for the central term of the equation. Look at the third and fourth equations. multiplying 6 and 5 will give you 30, but when combining terms, if they are both the same sign you will get 11, if they are different signs you will get 1.
(x - 5) (x + 6) = x^2 +6x -5x -30 (multiplying each term of each parentheses by each term of the other parentheses) (x times x, x times 6, -5 times x, -5 times 6)
x^2 -5x +6x -30 = x^2 +x - 30 (combining like terms)
They just want you to factor them.
For example, take x^2 + 20x + 99. In order to factor, you need to find two numbers whose product is 99 and whose sum is 20. List the factors of 99: 11 an 9; 99 and 1; 3 and 33. Which set from this list adds to 20? 11 and 9
Then, you plug the two numbers you chose into the general formula: (x + a)(x + b)
In this case, a = 9 and b = 11
The answer is (x + 9)(x + 11)
You should be able to get the rest!
Note: if the question was x^2 + 20x + 99 = 0, then you set the factorization equal to 0: (x + 9)(x + 11) = 0
In this case, the equation is true when x = -9 and x = -11
x2 +20x + 99
(x + 11) (x + 9)
x2 - 3x -88
(x -11) (x +3)
Gee, I hope this isn't for homework!
I feel funny about giving you the rest...
use the quadratic equation to solve them...you can do a google search for the equation (i can't type it in here) and then you just plug the numbers in