Divide 3x³ + x² + 2x + 5 by 1 + 2x +x²
Answers
Remainder = 9x + 10
What is a polynomial?
An expression which is composed of variables, constants and exponents that are composed using mathematical operations such as addition, subtraction, multiplication and division.
Polynomial Division
Firstly, in division,
divisor ) dividend ( quotient
- The Dividend is the number that is to be divided by the divisor.
- The number by which the dividend is to be divided is called the divisor.
- The result obtained by the division is called the quotient.
- The number that remains after division is called the remainder.
Steps to solve
1. Arrange the given polynomial in the decreasing order of their degrees.
2. Choose a quotient in such a way that, when multiplied with the divisor, it cancels the first term of the dividend.
3. Subtract the terms multiplied and bring down one term to continue the process.
4. Stop the division when the degree of remainder is less than that of the divisor.
Let us divide 3x³ + x² + 2x + 5 by 1 + 2x +x² using the above steps,
x²+ 2x + 1 ) 3x³ + x² + 2x + 5 ( 3x
3x³ + 2x² +3x
0 +( x²-2x² ) + (2x-3x)
Here 3x is the quotient, because when we multiply 3x and x² we get 3x³. 3x³ is the first term of the dividend ⇒ They cancel out as shown above.
Let us take 5 and now to get -x² we need to take -1 in the quotient.
x²+ 2x + 1 ) 3x³ + x² + 2x + 5 ( 3x -5
3x³ + 6x² + 3x
0 - 5x² - x + 5
- 5x² -10x -5
9x + 10
∴ On dividing 3x³ + x² + 2x + 5 by 1 + 2x +x²
Quotient = 3x - 5
Remainder = 9x + 10
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