how do you factor 20x^2-4x-144
Your School Subject is Math, not "home."
20x^2-4x-144
= 4(5x^2 - x - 36)
there are no factors of the quadratic using rational numbers.
To factor the quadratic expression 20x^2 - 4x - 144, follow these steps:
Step 1: Check for the greatest common factor (GCF)
Look for a common factor that can be factored out from all the terms. In this case, there is no common factor other than 1, so we move on to the next step.
Step 2: Check if it is a perfect square trinomial or a difference of squares
If the quadratic expression is a perfect square trinomial (e.g., x^2 + 2xy + y^2) or a difference of squares (e.g., a^2 - b^2), it can be factored further using those formulas. However, our expression does not fall into either category.
Step 3: Factor by grouping or using the quadratic formula
Since our quadratic expression does not fit the previous categories, we need to factor it using another method. In this case, we'll use factoring by grouping.
Step 4: Factor by grouping
We'll break the middle term (-4x) into two terms whose coefficients multiply to give the product of the leading coefficient (20) and the constant term (-144) while adding up to the coefficient of the middle term (-4x).
Product: (a * c) = (20 * -144) = -2880
Sum: (b) = -4x
We need to find two numbers that multiply to -2880 and add up to -4. With some trial and error or using a factoring calculator, we find that the numbers are -80 and 36.
To factor by grouping, rewrite the quadratic with these new terms:
20x^2 - 80x + 36x - 144
Now, we can group the terms:
(20x^2 - 80x) + (36x - 144)
Step 5: Factor out the greatest common factor (GCF) from each group
The GCF of the first group is 20x, and the GCF of the second group is 36.
20x(x - 4) + 36(x - 4)
Step 6: Factor out the common binomial factor
Now we have a common binomial factor (x - 4) that we can factor out.
(x - 4)(20x + 36)
Therefore, the factored form of the quadratic expression 20x^2 - 4x - 144 is (x - 4)(20x + 36).