Divide 5x^4 - 3x^2 + 8x + 6 by x^2 + 8
My answer was 5x^2 - 43 with a remainder of 8x - 338. Is this correct?
I have the same quotient, but the remainder is 8x+350.
Can you check your calculations?
How do I get 350?
Nevermind i added wrong. I got it. Thanks!!
To check if your answer is correct, we can use long division to divide 5x^4 - 3x^2 + 8x + 6 by x^2 + 8.
Let's start by writing the division problem in long division format:
_______________________________________
x^2 + 8 | 5x^4 - 3x^2 + 8x + 6
To begin, we divide the first term of the dividend (5x^4) by the first term of the divisor (x^2). This gives us 5x^2 as the first term of the quotient. We then multiply this quotient by the divisor (x^2 + 8) and subtract it from the dividend:
5x^2
___________
x^2 + 8 | 5x^4 - 3x^2 + 8x + 6
- (5x^2 * x^2 + 5x^2 * 8)
Performing the subtraction, we get:
5x^2
___________
x^2 + 8 | 5x^4 - 3x^2 + 8x + 6
- (5x^4 + 40x^2)
___________________
-43x^2 + 8x + 6
Now, we bring down the next term, which is 8x, and repeat the process:
5x^2 - 43
______________
x^2 + 8 | 5x^4 - 3x^2 + 8x + 6
- (5x^4 + 40x^2)
___________________
-43x^2 + 8x + 6
- (-43x^2 - 344)
_____________________________
352x + 6
Lastly, we bring down the last term, which is 6, and perform the division one final time:
5x^2 - 43
______________
x^2 + 8 | 5x^4 - 3x^2 + 8x + 6
- (5x^4 + 40x^2)
___________________
-43x^2 + 8x + 6
- (-43x^2 - 344)
_____________________________
352x + 6
At this point, we cannot perform any more divisions since the degree of 352x is higher than the degree of x^2 + 8. Therefore, the polynomial 5x^2 - 43 is the quotient, and the polynomial 352x + 6 is the remainder.
Comparing this to your answer of 5x^2 - 43 with a remainder of 8x - 338, we see that the quotients are the same, but the remainders are different. Therefore, it seems that your remainder is incorrect.
The correct answer is:
Quotient: 5x^2 - 43
Remainder: 352x + 6