How do you divide #(x^4  7x^3 + 2x^2 + 9x)/(x^3x^2+2x+1)#?
Long divide the coefficients to find:
#(x^47x^3+2x^2+9x)/(x^3x^2+2x+1) = x6 + (6x^2+4x+6)/(x^3x^2+2x+1)#
That is, the quotient is
I like to long divide the coefficients, not forgetting to include
The process is similar to long division of numbers.
Write the dividend (
Choose the first term
Write out the product of this first term of the quotient and the divisor below the dividend and subtract it.
Bring down the next term (
Choose the next term
Write out the product of this second term of the quotient and the divisor below the remainder and subtract it.
The resulting remainder
In this example, we find the quotient is
By signing up, you agree to our Terms of Service and Privacy Policy
To divide (x^4  7x^3 + 2x^2 + 9x) by (x^3  x^2 + 2x + 1), you can use long division. Here are the steps:

Divide the highest degree term of the numerator (x^4) by the highest degree term of the denominator (x^3). The result is x.

Multiply the entire denominator (x^3  x^2 + 2x + 1) by the result from step 1 (x). This gives you x^4  x^3 + 2x^2 + x.

Subtract the result from step 2 from the numerator (x^4  7x^3 + 2x^2 + 9x). This gives you 6x^3 + 9x.

Bring down the next term from the numerator (6x^3 + 9x). This gives you 6x^3 + 9x + 0.

Divide the highest degree term of the new numerator (6x^3) by the highest degree term of the denominator (x^3). The result is 6x^2.

Multiply the entire denominator (x^3  x^2 + 2x + 1) by the result from step 5 (6x^2). This gives you 6x^3 + 6x^2  12x  6.

Subtract the result from step 6 from the new numerator (6x^3 + 9x + 0). This gives you 15x^2  3x  6.

Bring down the next term from the numerator (15x^2  3x  6). This gives you 15x^2  3x  6 + 0.

Divide the highest degree term of the new numerator (15x^2) by the highest degree term of the denominator (x^3). The result is 0.

Multiply the entire denominator (x^3  x^2 + 2x + 1) by the result from step 9 (0). This gives you 0.

Subtract the result from step 10 from the new numerator (15x^2  3x  6 + 0). This gives you 15x^2  3x  6.
Since the degree of the new numerator (15x^2  3x  6) is less than the degree of the denominator (x^3  x^2 + 2x + 1), the division is complete. The quotient is x  6x^2 and the remainder is 15x^2  3x  6.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7