divide -3x^3-4x^2+4x+3 by x-2
In google paste:
polynomial division calculator
When you see list of results click on:
Polynomial Long Division Calculator eMathHelp
When page be open in rectangle Divide (dividend) type:
-3x^3-4x^2+4x+3
In rectagle By (divisor) type x-2
Then click option CALCULATE
You will see solution step-by-step
It can be like this, but the professor won't believe you did it.
( - 3 x³ - 4 x² + 4 x + 3 ) / ( x - 2 ) = - ( 3 x³ + 4 x² - 4 x - 3 ) / ( x - 2 ) =
- ( 3 x³ + 4 x² - 4 x - 3 + 10 x² - 10 x² + 20 x - 20 x + 32 - 32 ) / ( x - 2 ) =
- ( 3 x³ + 4 x² - 4 x + 10 x² - 10 x² + 20 x - 20 x + 32 - 32 - 3 ) / ( x - 2 ) =
- ( 3 x³ + 4 x² - 10 x² + 10 x² - 4 x + 20 x - 20 x - 32 + 32 - 3 ) / ( x - 2 ) =
- ( 3 x³ - 6 x² + 10 x² + 16 x - 20 x - 32 + 29 ) / ( x - 2 ) =
- ( 3 x³ - 6 x² + 10 x² - 20 x + 16 x - 32 + 29 ) / ( x - 2 ) =
- [ 3 x² ( x - 2 ) + 10 x ( x - 2 ) + 16 ( x - 2 ) + 29 ] / ( x - 2 ) =
- [ 3 x² ( x - 2 ) / ( x - 2 ) + 10 x ( x - 2 ) / ( x - 2 ) + 16 ( x - 2 ) / ( x - 2 ) + 29 / ( x - 2 ) ] =
- [ 3 x² + 10 x + 16 + 29 / ( x - 2 ) ] = - 3 x² - 10 x - 16 - 29 / ( x - 2 )
( - 3 x³ - 4 x² + 4 x + 3 ) / ( x - 2 ) = - 3 x² - 10 x - 16 - 29 / ( x - 2 )
Why did the polynomial go to the therapist? Because it had commitment issues with the divisor x-2!
All joking aside, let's solve the division problem.
Using long division, we have:
-3x^2 + 2x + 8
_______________________
x - 2 | -3x^3 - 4x^2 + 4x + 3
-(-3x^3 + 6x^2)
---------------
-10x^2 + 4x
+10x^2 - 20x
---------------
24x + 3
-24x + 48
--------------
-45
The result of dividing -3x^3 - 4x^2 + 4x + 3 by x - 2 is -3x^2 + 2x + 8 with a remainder of -45.
To divide the polynomial -3x^3 - 4x^2 + 4x + 3 by x - 2, we can use long division method. Here are the step-by-step instructions:
Step 1: Divide the first term of the dividend by the first term of the divisor. Write the result above the line.
-3x^3 ÷ x = -3x^2
-3x^2
x - 2 | -3x^3 - 4x^2 + 4x + 3
Step 2: Multiply the divisor by the result of step 1, and write the product below the dividend term.
-3x^2 * (x - 2) = -3x^3 + 6x^2
-3x^2
x - 2 | -3x^3 - 4x^2 + 4x + 3
-3x^3 + 6x^2
Step 3: Subtract the product from step 2 from the appropriate terms of the dividend, and write the result below the line.
(-3x^3 - 4x^2 + 4x + 3) - (-3x^3 + 6x^2) = -10x^2 + 4x + 3
-3x^2
x - 2 | -3x^3 - 4x^2 + 4x + 3
-3x^3 + 6x^2
_______________
-10x^2 + 4x + 3
Step 4: Bring down the next term from the dividend.
-10x^2 + 4x + 3
-3x^2
x - 2 | -3x^3 - 4x^2 + 4x + 3
-3x^3 + 6x^2
_______________
-10x^2 + 4x + 3
-10x^2 + 20x
Step 5: Repeat steps 1 to 4 until there are no more terms to bring down.
-10x^2 ÷ x = -10x
-3x^2 - 10x
x - 2 | -3x^3 - 4x^2 + 4x + 3
-3x^3 + 6x^2
_______________
-10x^2 + 4x + 3
-10x^2 + 20x
_________
-16x + 3
Step 6: The division is complete. The remainder is -16x + 3.
Therefore, the result of dividing -3x^3 - 4x^2 + 4x + 3 by x - 2 is:
Quotient: -3x^2 - 10x
Remainder: -16x + 3
To divide the polynomial -3x^3 - 4x^2 + 4x + 3 by x - 2, we can use long division.
Here's the step-by-step process to divide these polynomials:
Step 1: Write the dividend (the polynomial we're dividing) and the divisor (x - 2) in long division format:
__________________
x - 2 | -3x^3 - 4x^2 + 4x + 3
Step 2: Divide the first term of the dividend (-3x^3) by the first term of the divisor (x). This gives us -3x^2.
Write this quotient above the division bar, aligned with the x^2 term:
___________________
x - 2 | -3x^3 - 4x^2 + 4x + 3
-3x^2
Step 3: Multiply the divisor (x - 2) by the quotient (-3x^2) and write the result under the dividend, subtracting it as well:
-3x^2(x - 2) = -3x^3 + 6x^2
__________________
x - 2 | -3x^3 - 4x^2 + 4x + 3
-3x^2(x - 2)
-3x^3 + 6x^2
______________
Step 4: Subtract the result from the previous step (-3x^3 + 6x^2) from the dividend (-3x^3 - 4x^2 + 4x + 3). This gives us a new polynomial:
-3x^3 - 4x^2 + 4x + 3 - (-3x^3 + 6x^2)
-3x^3 - 4x^2 + 4x + 3 + 3x^3 - 6x^2
Step 5: Combine like terms in the new polynomial:
-3x^3 + 3x^3 - 4x^2 - 6x^2 + 4x + 3
0x^3 - 10x^2 + 4x + 3
Step 6: We now repeat the process with the new polynomial (0x^3 - 10x^2 + 4x + 3) divided by x - 2:
__________________
x - 2 | -3x^3 - 4x^2 + 4x + 3
-3x^2(x - 2)
-3x^3 + 6x^2
______________
- 10x^2 + 4x + 3
Step 7: Divide the first term of the new polynomial (-10x^2) by the first term of the divisor (x). This gives us -10x.
Write this quotient above the division bar, aligned with the x term:
___________________
x - 2 | -3x^3 - 4x^2 + 4x + 3
-3x^2(x - 2)
-3x^3 + 6x^2
______________
-10x^2 + 4x + 3
-10x^2
Step 8: Multiply the divisor (x - 2) by the new quotient (-10x) and write the result under the polynomial, subtracting it as well:
-10x(x - 2) = -10x^2 + 20x
__________________
x - 2 | -3x^3 - 4x^2 + 4x + 3
-3x^2(x - 2)
-3x^3 + 6x^2
-10x^2 + 20x
______________
16x + 3
Step 9: Subtract the result from the previous step (16x + 3) from the last polynomial (-10x^2 + 4x + 3). This gives us a new polynomial:
-10x^2 + 4x + 3 - (16x + 3)
-10x^2 + 4x + 3 - 16x - 3
Step 10: Combine like terms in the new polynomial:
-10x^2 - 16x + 4x + 3 - 3
-10x^2 - 12x
Step 11: There are no more terms to divide.
The remainder is -10x^2 - 12x.
Therefore, the result of dividing -3x^3 - 4x^2 + 4x + 3 by x - 2 is:
Quotient: -3x^2 - 10x
Remainder: -10x^2 - 12x