what must be subtracted from the polynomial 4x^3+2x^2+5x-6 so that the resulting polynomial is divided by 2x^2+3x+1
Answers
9x -4
Step-by-step explanation:
Let's divide the given polynomial by 2x^2+3x+1 to find out the remainder.
4x^3 + 2x^2 + 5x - 6 / 2x^2+3x+1
4x^3 + 6x^2 + 2x
- 4x^2 + 3x - 6
- 4x^2 - 6x - 2
9x - 4
The remainder is 9x-4.
If 9x -4 is subtracted from the given polynomial, then the resulting resulting polynomial will be is divisible by 2x^2+3x+1.
Given : polynomial 4x³ +2x² + 5x - 6 & 2x² + 3x + 1 Divisor
To find : what must be subtracted from the polynomial so that the resulting polynomial is completely Divisible
Solution:
a = bx + r
=> a - r = bx
a = 4x³ +2x² + 5x - 6
b = 2x² + 3x + 1
Hence subtracting remainder from the polynomial will make resulting polynomial to be divided by 2x² + 3x + 1
2x - 2
2x² + 3x + 1 _| 4x³ +2x² + 5x - 6 |_
4x³ + 6x² + 2x
________________
-4x² + 3x - 6
-4x² -6x - 2
___________
9x - 4
Hence 9x - 4 to be Subtracted from 4x³ +2x² + 5x - 6 so that
resulting polynomial is divided by 2x² + 3x + 1
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