how to divide and simplify
12x^3-22x^2-44x-16/6x+4
You can use either long division method or Horner.
-2/3 | 12 -22 -44 -16
| -8 -20 128/3
---------------------
12 -30 -64 80/3
Quotient = 12x^2 - 30x - 64
Remainder = 80/3
Or, you can write as:
12x^3 - 22x^2 - 44x - 16 / 6x+4 = 12x^2 - 30x - 64 + (80/3)/(6x+4)
Now, use the long division method by yourself as a practice
Oops... Sorry. I've made a few errors in my calculation. Should be:
-2/3 | 12 -22 -44 -16
| -8 20 16
----------------
12 -30 -24 0
Since the denominator has 1 degree of polynomial and its coefficient is 6, we divide the quotient with 6. So, we have:
Quotient = 2x^2 - 5x - 4
To divide and simplify the expression (12x^3 - 22x^2 - 44x - 16) by (6x + 4), follow these steps:
Step 1: Factor both the numerator and the denominator as much as possible:
12x^3 - 22x^2 - 44x - 16 = 4(3x^3 - 5.5x^2 - 11x - 4)
6x + 4 = 2(3x + 2)
Step 2: Identify any common factors between the numerator and the denominator. In this case, both terms have a factor of 2.
Step 3: Divide both the numerator and the denominator by the common factor to simplify the expression:
(4(3x^3 - 5.5x^2 - 11x - 4))/(2(3x + 2)) = 2(3x^3 - 5.5x^2 - 11x - 4)/(3x + 2)
Now the expression is simplified and cannot be further reduced.