Need help on factoring. HOw exactly would I solve these(big test coming up):
-3x to the second+18x+12
-5x to the second-13x=6
-5x to the second-6x=1
-and xto the second + 6x=10
I can't use the quadratic equation. I have to use the a times c method.
Two things:
1. I think your first equation has a typo, since it is not an equation
2. I think you are using the - in front of each equation not as a negative sign, but rather as a dash. Why????
So I will assume that your second equation is
5x^2 - 13x = 6 (the ^ means 'to the exponent')
5x^2 - 13x - 6 = 0
(a)(c) = 5(-6) = -30
now look for factors of -30 which have a sum of -13
that would be -15 and 2
check :(-15)(2) = -30, -15 + 2 = -13
now replace the middle term of -13x with -15x+2x
5x^2 - 15x + 2x - 6 = 0
take out a common factor from the first two terms, and from the last two terms
5x(x-3) + 2(x-3) = 0
now x-3 is a common factor, so ...
(x-3)(5x+2) = 0
x-3 = 0 or 5x+2 = 0
x = 3 or x = -2/5
Do the others the same way
So You using the quadratic or a time c method will give me the same answer?
To solve these quadratic equations, you will need to use the factoring method. Let's break down the steps for each equation.
1. -3x^2 + 18x + 12:
First, check if there is a common factor. In this case, there is a common factor of -3. Divide each term by -3 to simplify the equation:
-x^2 + 6x - 4.
Now, we need to factor the quadratic trinomial. You are permitted to use the "a times c" method, so consider the product of the first and last coefficients:
The product of -1 and -4 is 4.
Next, find two numbers that multiply to give you the product (4) and add up to the coefficient of the middle term (6). In this case, the numbers are 2 and 2.
Rewrite the equation using these numbers to split the middle term:
-x^2 + 2x + 2x - 4.
Now, group the terms and factor each one:
x(x - 2) + 2(x - 2).
Finally, notice the common binomial factor (x - 2) and factor it out:
(x - 2)(x + 2) is the factored form of the equation.
2. -5x^2 - 13x + 6:
Divide each term by -1 to simplify:
5x^2 + 13x - 6.
Again, let's find the product of the first and last coefficients:
The product of 5 and -6 is -30.
Now, find two numbers that multiply to give you -30 and add up to 13. The numbers are 15 and -2.
Rewrite the equation:
5x^2 + 15x - 2x - 6.
Group and factor:
5x(x + 3) - 2(x + 3).
Notice the common binomial factor (x + 3):
(x + 3)(5x - 2) is the factored form.
3. -5x^2 - 6x + 1:
Divide each term by -1:
5x^2 + 6x - 1.
Get the product of the first and last coefficients:
The product of 5 and -1 is -5.
Find two numbers that multiply to give you -5 and add up to 6. The numbers are 5 and 1.
Rewrite the equation:
5x^2 + 5x + x - 1.
Group and factor:
5x(x + 1) + (x + 1).
Notice the common binomial factor (x + 1):
(x + 1)(5x + 1) is the factored form.
4. x^2 + 6x - 10:
This equation is already in standard form, so we can go straight to factoring.
Get the product of the first and last coefficients:
The product of 1 and -10 is -10.
Find two numbers that multiply to give you -10 and add up to 6. The numbers are 10 and -4.
Rewrite the equation:
x^2 + 10x - 4x - 10.
Group and factor:
x(x + 10) - 2(x + 10).
Notice the common binomial factor (x + 10):
(x + 10)(x - 2) is the factored form.
Remember to always double-check your factored equations by expanding and simplifying them to ensure correctness.