Question

divide.
\\((4x^2 + 11x - 17) \div (x + 4)\\)
your answer should give the quotient and the remainder.
quotient: \\(square\\)
remainder: \\(square\\)

Explanation:

Step1: Use polynomial long division

Divide the leading term of the dividend \(4x^2\) by the leading term of the divisor \(x\), we get \(4x\). Multiply the divisor \(x + 4\) by \(4x\), we have \(4x(x + 4)=4x^2+16x\). Subtract this from the dividend: \((4x^2 + 11x - 17)-(4x^2+16x)=4x^2 + 11x - 17 - 4x^2 - 16x=-5x - 17\).

Step2: Divide the new leading term

Now, divide the leading term of \(-5x\) by the leading term of \(x\), we get \(-5\). Multiply the divisor \(x + 4\) by \(-5\), we have \(-5(x + 4)=-5x-20\). Subtract this from \(-5x - 17\): \((-5x - 17)-(-5x - 20)=-5x - 17 + 5x + 20 = 3\).

Answer:

Quotient: \(4x - 5\)
Remainder: \(3\)