Factor the polynomial completely
3m^2 -75
This is how I started to work it out.
(3m-23)(m-5)
Start by factoring out the GCF, which in this case is 3.
So you get
3m²-75
=3(m²-25)
The part in parentheses is the difference of two squares. Look up your course notes to see how to factor this part, namely using the standard form:
(A²-B²) = (A+B)(A-B)
To factor the polynomial 3m^2 - 75 completely, you need to find the common factors of both terms. In this case, both terms have a common factor of 3.
Step 1: Begin by factoring out the common factor of 3:
3(m^2 - 25)
Step 2: Notice that the expression within the parentheses is a difference of squares, as it can be written as (m)^2 - (5)^2. You can use the formula a^2 - b^2 = (a + b)(a - b) to further factor this expression.
Step 3: Apply the formula to factor (m^2 - 25):
3(m + 5)(m - 5)
Therefore, the completely factored form of the polynomial 3m^2 - 75 is 3(m + 5)(m - 5).