Solve by factoring:
1.) x^2 - x - 12 = 0
What are the factors of 12? (6 & 2, 3 & 4)
Which combination of those will add to -1?
(x - 4)(x + 3) = 0
x = 4 or -3
First in these type of problems if there is a variable that is squared i always start by putting those in first
1) (x ) (x )
then i decide if im going to need a - or + and in this case because we want to make it - we have to put one of each
2)(x- )(x+ )
then i just start by plugging in numbers and the correct answer i found was..
(x-4)(x+3)
if you need help on others just post em:)
of yes. sorry i almost forget
whenever solving for x
take the problem
(x-4)(x+3)
and make each their own equation
1) (x-4)=0
2)(x+3)=0
then add the 4 and the subtract the three and you get
x=4,-3
To solve the quadratic equation x^2 - x - 12 = 0 by factoring, we need to find two binomials whose product is equal to the quadratic equation.
Step 1: Write the equation in the form of ax^2 + bx + c = 0.
In this case, the equation is already in this form as x^2 - x - 12 = 0.
Step 2: Factor the quadratic equation into two binomials.
In order to factor the quadratic equation, we need to find two numbers whose product is equal to the constant term (-12) and whose sum is equal to the coefficient of the linear term (-1).
Let's try to find two numbers that fit these conditions:
The factors of 12 are:
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
Since we need to find two numbers whose sum is -1 (the coefficient of the linear term), the pair of numbers that satisfies this condition is 3 and -4, because 3 + (-4) = -1.
Step 3: Rewrite the equation using the factored form.
We can rewrite the quadratic equation as follows:
x^2 + 3x - 4x - 12 = 0
Step 4: Group the terms.
Now, let's group the terms:
(x^2 + 3x) + (-4x - 12) = 0
Step 5: Factor by grouping.
Factor out the greatest common factor from each group:
x(x + 3) - 4(x + 3) = 0
Step 6: Factor out the common binomial (x + 3).
(x - 4)(x + 3) = 0
Step 7: Set each factor equal to zero and solve for x.
We have two possible solutions:
x - 4 = 0 or x + 3 = 0
By solving each equation, we find the solutions:
x = 4 or x = -3
Therefore, the solutions to the quadratic equation x^2 - x - 12 = 0 are x = 4 and x = -3.