(8x^3 - 14x^2 - 27x - 9) / (4x + 3)
Do a long division, it works out exactly
I know to do long division but i still cant figure out how to divide a polynomial by a polynomial
It is sort of hard to show the steps in this format, but
here is a short video by Khan which shows the steps you have to take
http://www.youtube.com/watch?v=4u8_AMacu-Y
To divide the polynomial (8x^3 - 14x^2 - 27x - 9) by (4x + 3), you can use long division. Here's how you can approach it step by step:
Step 1: Start by dividing the highest degree term of the numerator by the highest degree term of the denominator. In this case, divide 8x^3 by 4x. The result is 2x^2.
2x^2
___________
4x + 3 | 8x^3 - 14x^2 - 27x - 9
Step 2: Multiply the divisor (4x + 3) by the quotient you just found (2x^2), and subtract it from the numerator:
2x^2 * (4x + 3) = 8x^3 + 6x^2
(8x^3 - 14x^2 - 27x - 9) - (8x^3 + 6x^2) = -20x^2 - 27x - 9
Step 3: Now, bring down the next term from the numerator, which is -20x^2. Divide it by the highest degree term of the denominator, which is 4x. The result is -5x.
2x^2 - 5x
___________
4x + 3 | 8x^3 - 14x^2 - 27x - 9
- (8x^3 + 6x^2)
______________
-20x^2 - 27x - 9
Step 4: Multiply the divisor (4x + 3) by the quotient (-5x), and subtract it from the current remainder:
-5x * (4x + 3) = -20x^2 - 15x
(-20x^2 - 27x - 9) - (-20x^2 - 15x) = -12x - 9
Step 5: Bring down the next term from the numerator, which is -12x. Divide it by the highest degree term of the denominator, which is 4x. The result is -3.
2x^2 - 5x - 3
___________
4x + 3 | 8x^3 - 14x^2 - 27x - 9
- (8x^3 + 6x^2)
______________
-20x^2 - 27x - 9
- (-20x^2 - 15x)
______________
-12x - 9
Step 6: Multiply the divisor (4x + 3) by the quotient (-3), and subtract it from the current remainder:
-3 * (4x + 3) = -12x - 9
(-12x - 9) - (-12x - 9) = 0
Step 7: The current remainder is 0, which means there is no more to divide. The final result is the quotient we obtained:
Quotient: 2x^2 - 5x - 3
Therefore, the division of (8x^3 - 14x^2 - 27x - 9) by (4x + 3) is equal to 2x^2 - 5x - 3.