Question

polynomial division box method (level 2)
score: 0/2 penalty: none
question
fill in the missing values below to find the quotient when ( 3x^4 + 4x^3 - 3x^2 - x - 6 ) is divided by ( x + 2 ).
answer attempt 1 out of 5
( (3x^4 + 4x^3 - 3x^2 - x - 6) div (x + 2) = )

Explanation:

Step1: Divide the leading term

Divide the leading term of the dividend \(3x^4\) by the leading term of the divisor \(x\), we get \(3x^3\). This will be the first term of the quotient.

Step2: Multiply and subtract

Multiply the divisor \(x + 2\) by \(3x^3\) to get \(3x^4+6x^3\). Subtract this from the dividend: \((3x^4 + 4x^3-3x^2 - x - 6)-(3x^4+6x^3)=-2x^3-3x^2 - x - 6\).

Step3: Divide the new leading term

Divide the leading term of the new dividend \(-2x^3\) by \(x\), we get \(-2x^2\). This is the second term of the quotient.

Step4: Multiply and subtract

Multiply \(x + 2\) by \(-2x^2\) to get \(-2x^3-4x^2\). Subtract this from the new dividend: \((-2x^3-3x^2 - x - 6)-(-2x^3-4x^2)=x^2 - x - 6\).

Step5: Divide the new leading term

Divide the leading term of the new dividend \(x^2\) by \(x\), we get \(x\). This is the third term of the quotient.

Step6: Multiply and subtract

Multiply \(x + 2\) by \(x\) to get \(x^2+2x\). Subtract this from the new dividend: \((x^2 - x - 6)-(x^2+2x)=-3x - 6\).

Step7: Divide the new leading term

Divide the leading term of the new dividend \(-3x\) by \(x\), we get \(-3\). This is the fourth term of the quotient.

Step8: Multiply and subtract

Multiply \(x + 2\) by \(-3\) to get \(-3x-6\). Subtract this from the new dividend: \((-3x - 6)-(-3x - 6)=0\).

So the quotient is \(3x^3-2x^2+x - 3\).

Answer:

\(3x^3-2x^2+x - 3\)