what is the factored form of 12x^2 - 75
A: 3(2x + 5)^2
B: 3(2x + 5) (2x - 5)
C: 3(2x - 5)^2
D: 3(5x + 2) (5x - 2)
idk where to start. Help please.
Well, your first step obviously is to look for a common factor, do that
after that .......
- does the difference of squares ring a bell?
If i'm supposed to be looking for a common factor in 12 and 75, i can find anything that isn't a decimal?
or is it supposed to be 75 and 144, seeing as 12 squared is 144
Common factor out the 3 : )
3(4) = 12
and 3(25) = 75
then you have a difference of squares left : )
= 3(4x^2 - 25)
= ... now factor with a difference of squares : )
so is the answer C? i may be wrong because i'm a lil bit rusty when it comes to difference of squares.
oh or is it B?
WHen you expand B and C which one gives you the 4x^2 - 25
Only one of them does : )
To find the factored form of the quadratic equation 12x^2 - 75, we can use the method of factoring by grouping. Here are the steps:
Step 1: Look for a common factor in the expression. In this case, both terms have a common factor of 3, so we can factor it out:
12x^2 - 75 = 3(4x^2 - 25)
Step 2: Observe that the expression inside the parentheses is a difference of squares. It can be factored as (a^2 - b^2) = (a + b)(a - b). In this case, a = 2x and b = 5:
4x^2 - 25 = (2x)^2 - 5^2 = (2x + 5)(2x - 5)
Step 3: Substitute the factored form of the difference of squares back into the original expression:
3(4x^2 - 25) = 3(2x + 5)(2x - 5)
Therefore, the factored form of 12x^2 - 75 is option B: 3(2x + 5)(2x - 5).