Divide 3x^3 + 3x^2 + 2x – 2 by x + 3 using long division. Check my answer please.
3x^2 – 6x + 20
3x^2 + 12x – 16
3x^2 + 12x – 16, R 58
3x^2 – 6x + 20, R -62 (I think that it's this one)
I agree
To divide 3x^3 + 3x^2 + 2x - 2 by x + 3 using long division, follow these steps:
Step 1: Divide the first term of the numerator (3x^3) by the first term of the denominator (x).
This gives 3x^2 as the first term of the quotient.
Step 2: Multiply the entire denominator (x + 3) by the first term of the quotient (3x^2).
This gives (3x^2)(x + 3) = 3x^3 + 9x^2.
Step 3: Subtract the result from the numerator.
3x^3 + 3x^2 + 2x - 2 - (3x^3 + 9x^2) = -6x^2 + 2x - 2.
Step 4: Bring down the next term of the numerator (-6x^2).
Now the expression becomes -6x^2 + 2x - 2.
Step 5: Repeat steps 1-4 until there are no more terms to bring down or the degree of the numerator is lower than the denominator.
Using the steps above, the correct answer would be:
3x^2 - 6x + 20, R -62
So, your initial guess was correct. The remainder is -62, not 58.
To divide the polynomial 3x^3 + 3x^2 + 2x - 2 by x + 3 using long division, you can follow these steps:
Step 1: Write the dividend (3x^3 + 3x^2 + 2x - 2) and the divisor (x + 3) in long division format:
___________________
(x + 3) | 3x^3 + 3x^2 + 2x - 2
Step 2: Divide the first term of the dividend (3x^3) by the first term of the divisor (x) to get the quotient's first term. Place this term above the division bar and multiply it by the divisor:
3x^2
___________________
(x + 3) | 3x^3 + 3x^2 + 2x - 2
3x^3 + 9x^2
Step 3: Subtract the product from step 2 (3x^3 + 9x^2) from the dividend (3x^3 + 3x^2 + 2x - 2). This will give you the new dividend:
3x^2
___________________
(x + 3) | 3x^3 + 3x^2 + 2x - 2
- (3x^3 + 9x^2)
______________
-6x^2 + 2x - 2
Step 4: Bring down the next term of the dividend (2x) and repeat steps 2 and 3:
3x^2 - 6x
___________________
(x + 3) | 3x^3 + 3x^2 + 2x - 2
- (3x^3 + 9x^2)
______________
-6x^2 + 2x - 2
- (-6x^2 - 18x)
_______________
20x - 2
Step 5: Bring down the last term of the dividend (-2), and repeat steps 2 and 3:
3x^2 - 6x + 20
___________________
(x + 3) | 3x^3 + 3x^2 + 2x - 2
- (3x^3 + 9x^2)
______________
-6x^2 + 2x - 2
- (-6x^2 - 18x)
_______________
20x - 2
- (20x + 60)
_________________
-62
According to your answers, the correct answer is: 3x^2 - 6x + 20 with a remainder of -62.