What is the result when 2x^3 -9x^2 +11x-6 is divided by x-3?
I have no idea how to even start solving this.
To solve this problem, we can use polynomial long division. Here are the step-by-step instructions:
Step 1: Write the dividend, 2x^3 - 9x^2 + 11x - 6, and the divisor, x - 3.
Step 2: Divide the first term of the dividend by the first term of the divisor. In this case, divide 2x^3 by x. The result is 2x^2.
Step 3: Multiply the divisor by the quotient obtained in step 2. Multiply (x - 3) by 2x^2. The result is 2x^3 - 6x^2.
Step 4: Subtract the product from step 3 from the dividend. Subtract (2x^3 - 6x^2) from (2x^3 - 9x^2 + 11x - 6). The result is -3x^2 + 11x - 6.
Step 5: Bring down the next term from the dividend, which is 11x.
Step 6: Repeat steps 2 to 5 until you have brought down all the terms from the dividend.
Step 7: Divide the first term of the new dividend (-3x^2 + 11x - 6) by the first term of the divisor (x - 3). In this case, divide -3x^2 by x. The result is -3x.
Step 8: Multiply the divisor by the new quotient obtained in step 7. Multiply (x - 3) by -3x. The result is -3x^2 + 9x.
Step 9: Subtract the product from step 8 from the new dividend. Subtract (-3x^2 + 9x) from (-3x^2 + 11x - 6). The result is 2x - 6.
Step 10: Bring down the next term from the new dividend, which is -6.
Step 11: Repeat steps 7 to 10 until you have brought down all the terms from the new dividend.
Step 12: Divide the first term of the new dividend (2x - 6) by the first term of the divisor (x - 3). In this case, divide 2x by x. The result is 2.
Step 13: Multiply the divisor by the new quotient obtained in step 12. Multiply (x - 3) by 2. The result is 2x - 6.
Step 14: Subtract the product from step 13 from the new dividend. Subtract (2x - 6) from (2x - 6). The result is 0.
Step 15: There is no remainder, and the division is complete.
Therefore, the result of dividing 2x^3 - 9x^2 + 11x - 6 by x - 3 is 2x^2 - 3x + 2.
To start solving this, you can use polynomial long division. Here's how you can proceed:
Step 1: Arrange the dividend (2x^3 - 9x^2 + 11x - 6) and the divisor (x - 3) in the long division format:
_________________________
x - 3 | 2x^3 - 9x^2 + 11x - 6
Step 2: Divide the first term of the dividend (2x^3) by the first term of the divisor (x), which gives you 2x^2. Write this above the line.
2x^2
_________________________
x - 3 | 2x^3 - 9x^2 + 11x - 6
Step 3: Multiply the divisor (x - 3) by the quotient (2x^2) and write the result below the dividend. Subtract this result from the dividend.
2x^2
_________________________
x - 3 | 2x^3 - 9x^2 + 11x - 6
-(2x^3 - 6x^2)
Subtraction:
2x^2 - 9x^2 = -7x^2
_________________________
x - 3 | 2x^3 - 9x^2 + 11x - 6
-(2x^3 - 6x^2)
_________________________
- 7x^2 + 11x - 6
Step 4: Bring down the next term from the original dividend, which is 11x.
2x^2 - 7x^2 + 11x
_________________________
x - 3 | 2x^3 - 9x^2 + 11x - 6
-(2x^3 - 6x^2)
_________________________
- 7x^2 + 11x - 6
Step 5: Repeat steps 2 to 4 until you have subtracted all terms of the dividend.
2x^2 - 7x^2 + 11x - 6
_________________________
x - 3 | 2x^3 - 9x^2 + 11x - 6
-(2x^3 - 6x^2)
_________________________
- 7x^2 + 11x - 6
7x^2 - 21x
_________________________
32x - 6
Step 6: Finally, write the remainder (32x - 6) above the divisor (x - 3) in fractional form. The division is complete!
2x^2 - 7x^2 + 11x - 6
_________________________
x - 3 | 2x^3 - 9x^2 + 11x - 6
-(2x^3 - 6x^2)
_________________________
- 7x^2 + 11x - 6
7x^2 - 21x
_________________________
32x - 6
Therefore, the result of dividing 2x^3 - 9x^2 + 11x - 6 by x - 3 is:
Quotient: 2x^2 - 7x^2 + 11x - 6
Remainder: 32x - 6
start by learning polynomial division. This handy online calculator will show you how things work.
http://calc101.com/webMathematica/long-divide.jsp
you probably never did "long division" by hand in grammar school
... this works the same way
or synthetic division
... it must have been explained before a problem like this
... google it