4x^3-5x^2-10x-3 divided by 4x+3
Read and apply this:
http://www.sosmath.com/algebra/factor/fac01/fac01.html
The first two terms should be x^2 -2x
There will me no remainder term
X^2-2X-1 is the complete answer
see site above for example
To divide the polynomial 4x^3 - 5x^2 - 10x - 3 by 4x + 3, we can use the long division method. Here's how to do it step-by-step:
Step 1: Write down the polynomial expression to be divided and the divisor:
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4x + 3 | 4x^3 - 5x^2 - 10x - 3
Step 2: Divide the highest-degree term of the dividend (4x^3) by the highest-degree term of the divisor (4x). The result is x^2 (x squared), which is the first term of the quotient. Write this above the line.
x^2
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4x + 3 | 4x^3 - 5x^2 - 10x - 3
Step 3: Multiply the entire divisor (4x + 3) with the first term of the quotient (x^2). Write the result below the line and subtract it from the original polynomial.
x^2
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4x + 3 | 4x^3 - 5x^2 - 10x - 3
- (4x^2 + 3x^2)
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- 2x^2 - 10x - 3
Step 4: Bring down the next term from the dividend (- 2x^2). This makes - 2x^2 the new dividend.
x^2
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4x + 3 | 4x^3 - 5x^2 - 10x - 3
- (4x^2 + 3x^2)
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- 2x^2 - 10x - 3
- ( - 2x^2 - 3)
Step 5: Divide the term with the highest degree in the new dividend (- 2x^2) by the highest-degree term of the divisor (4x). The result is - 1/2 (negative one-half), which becomes the next term of the quotient. Write this above the line.
x^2 - 1/2
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4x + 3 | 4x^3 - 5x^2 - 10x - 3
- (4x^2 + 3x^2)
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- 2x^2 - 10x - 3
- ( - 2x^2 - 3)
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- 7x - 3
Step 6: Multiply the entire divisor (4x + 3) with the newly found term of the quotient (- 1/2). Write the result below the line and subtract it from the new dividend.
x^2 - 1/2
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4x + 3 | 4x^3 - 5x^2 - 10x - 3
- (4x^2 + 3x^2)
______________
- 2x^2 - 10x - 3
- ( - 2x^2 - 3)
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- 7x - 3
- ( - 7/2x + 3/2)
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- 13/2
Step 7: The remainder -13/2 (negative thirteen over two) cannot be further divided by the divisor 4x + 3. Since there are no more terms in the dividend, we have completed the division.
Therefore, the quotient is x^2 - 1/2, and the remainder is -13/2 (in fraction form) or -6.5 (in decimal form).
So, the final result of dividing 4x^3 - 5x^2 - 10x - 3 by 4x + 3 is:
Quotient: x^2 - 1/2
Remainder: -13/2 or -6.5