How to factorise
3d³-12d²-15d
To factorize the expression 3d³ - 12d² - 15d, follow these steps:
Step 1: Identify the greatest common factor (GCF).
In this case, the largest common factor among the terms is 3d, so we can factor out 3d.
Step 2: Divide each term by the GCF.
Dividing 3d³ by 3d gives us d², dividing -12d² by 3d gives us -4d, and dividing -15d by 3d gives us -5.
So, our expression becomes:
3d(d² - 4d - 5)
Step 3: Factor the quadratic expression.
We now have a quadratic expression inside the parentheses: d² - 4d - 5. To factor this quadratic further, we need to find two numbers that add up to -4 (the coefficient of the middle term) and multiply to -5 (the constant term).
The factors of -5 that add up to -4 are -5 and 1. Thus, we can rewrite the quadratic expression as:
d² - 4d - 5 = (d - 5)(d + 1)
Now, we can factor out the expression completely:
3d(d - 5)(d + 1)
Therefore, the fully factorized form of 3d³ - 12d² - 15d is 3d(d - 5)(d + 1).
Step 1: Find the greatest common factor (GCF) of the terms.
The GCF of 3d³, -12d², and -15d is 3d.
Step 2: Rewrite the expression using the GCF.
3d(d² - 4d - 5)
Step 3: Factor the quadratic expression in the parentheses.
The quadratic expression can be factored as (d - 5)(d + 1).
Step 4: Rewrite the expression using the factored form.
3d(d - 5)(d + 1)
Therefore, the factored form of 3d³ - 12d² - 15d is 3d(d - 5)(d + 1).