what should be added to 2x4 +3x3-2x2-9x-12to be divisible by x2+3x+1
Answers
Answer:
21x + 17
Step-by-step explanation:
So you can find the answer by doing long division.
2x^4+3x^3-2x^2-9x-12/x^2 + 3x +1
You'll use the first factor of the divisor to divide the first factor of the dividend to find out the first part of the quotient.
2x^4/ x^2 = 2x^2
Then when you have the answer you will want to multiply the answer by the divisor.
2x^2(x^2+3x+1) = 2x^4+6x^3+2x^2
With this you have to multiply it by, -1.
-1(2x^4+6x^3+2x^2) = -2x^4 - 6x^3 - 2x^2
After you've done this you'll add the number you've gotten to the polynomial.
2x^4+3x^3-2x^2-9x-12 + (-2x^4) - 6x^3 - 2x^2 = -3x^3 - 4x^2 - 9x -12
The number you get from adding is the one you will continue with. Repeat all the steps until you get a remainder of 0 or can no longer divide the first factor of the dividend by the first factor of the divisor.
-3x^3 - 4x^2 - 9x -12/ x^2 + 3x +1
-3x^3/x^2 = -3x multiply by the divisor -3x(x^2 + 3x +1) = -6x^3 - 9x^2 - 3x
-1(-6x^3 - 9x^2 - 3x) = 6x^3 + 9x^2 + 3x
-3x^3 - 4x^2 - 9x -12 +-3x^3 - 4x^2 - 9x -12 = 5x^2 - 6x -12
5x^2 - 6x -12/ x^2 + 3x +1
5x^2/x^2 = 5
5(x^2 + 3x +1) = 5x^2 + 15x + 5 -1(5x^2 + 15x + 5)= -5x^2 - 15x -5
5x^2 - 6x -12 + (-5x^2) - 15x -5 = -21x - 17
-21x - 17, this is our remainder or what is keeping this equation from being divisible by, x^2 + 3x + 1. So to make the equation divisible by the divisor we have to add the opposite of the remainder to the equation in order to cancel it out.
The answer is, 21x + 17, because it is the opposite of, -21x - 17.
Step-by-step explanation:
hi here is your answer mate
