Trying to factor 2 equations
3x2+9x-30
4x2-4x-48
I assume you mean 3x² + 9x - 30
which on this board most people write as 3x^2 ...
=3(x^2 + 3x - 10)
=3(x+5)(x-2)
do the same thing for your second question, factor out the 4 first, then it's easy
Let me know what you got
4(x-4)(x+3)?
yup!
Thanks
To factor the first equation, 3x² + 9x - 30, you can use the method of factoring by grouping. Here's how you can approach it:
Step 1: Look for common factors and factor out the greatest common factor, if applicable. In this case, the greatest common factor is 3, so you can factor it out: 3(x² + 3x - 10).
Step 2: Now, you need to factor the quadratic expression inside the parentheses, x² + 3x - 10. To factor this quadratic expression, you need to find two numbers whose product is -10 and whose sum is 3.
Step 3: The numbers that fit this criteria are 5 and -2. So, rewrite the quadratic expression as follows: (x + 5)(x - 2).
Step 4: Combine the factored GCF and the factored quadratic expression: 3(x + 5)(x - 2). This is the fully factored form of the first equation.
Now, let's move on to factoring the second equation, 4x² - 4x - 48:
Step 1: Factor out the greatest common factor, which is 4: 4(x² - x - 12).
Step 2: Factor the quadratic expression inside the parentheses, x² - x - 12. To factor this quadratic expression, you need to find two numbers whose product is -12 and whose sum is -1.
Step 3: The numbers that satisfy these conditions are -4 and 3. Rewrite the quadratic expression accordingly: (x - 4)(x + 3).
Step 4: Combine the factored GCF and the factored quadratic expression: 4(x - 4)(x + 3). This is the fully factored form of the second equation.
So, the fully factored forms of the given equations are:
- First equation: 3(x + 5)(x - 2)
- Second equation: 4(x - 4)(x + 3)