Factor.
0.25x^2 + 0.3x + 0.09
I am having some trouble with this one. Please help if you can.
Thank you! :-)
To factor the quadratic expression 0.25x^2 + 0.3x + 0.09, we can use the factoring method.
Step 1: Start by multiplying the coefficient of x^2 (0.25) by the constant term (0.09). In this case, 0.25 * 0.09 = 0.0225.
Step 2: Next, we need to find two numbers that multiply to give us 0.0225 and add up to the coefficient of x (0.3). In this case, the two numbers are 0.15 and 0.15 because 0.15 * 0.15 = 0.0225 and 0.15 + 0.15 = 0.3.
Step 3: Now, we can rewrite the middle term (0.3x) as the sum of these two numbers. So, the expression can be written as:
0.25x^2 + 0.15x + 0.15x + 0.09.
Step 4: Group the terms:
(0.25x^2 + 0.15x) + (0.15x + 0.09).
Step 5: Factor by grouping.
Take out the greatest common factor from the first two terms and the last two terms separately:
x(0.25x + 0.15) + 0.15(0.25x + 0.15).
Step 6: Now, we can see that both terms have a common factor of (0.25x + 0.15). Factor it out:
(0.25x + 0.15)(x + 0.15).
Therefore, the factored form of the expression 0.25x^2 + 0.3x + 0.09 is (0.25x + 0.15)(x + 0.15).