Question

find the quotient and remainder using long division:

\\( \frac { 4 x ^ { 2 } + 10 x - 5 } { x + 3 } \\)

the quotient is

the remainder is

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Explanation:

Step1: Divide the leading term of the dividend by the leading term of the divisor

Divide \(4x^{2}\) by \(x\). \(\frac{4x^{2}}{x}=4x\). Multiply \((x + 3)\) by \(4x\): \(4x(x + 3)=4x^{2}+12x\). Subtract this from the dividend \((4x^{2}+10x - 5)-(4x^{2}+12x)=-2x-5\).

Step2: Divide the new leading term of the remaining polynomial by the leading term of the divisor

Divide \(-2x\) by \(x\). \(\frac{-2x}{x}=-2\). Multiply \((x + 3)\) by \(-2\): \(-2(x + 3)=-2x-6\). Subtract this from \(-2x - 5-(-2x - 6)=1\).

Answer:

The quotient is \(4x-2\), the remainder is \(1\).