Question

Divide using long division. Check your answer. (5x^2-3x+2) / (x-1) The quotient is _____ with remainder _____.

Answer 1

Long Division of Polynomials

Divide:

$5x^2-3x+2\text{ by }x-1$

Arranging dividend and divisor for the long division procedure:r thefrrrArA

$x-1\text{ \mid 5}x^2-3x+2$

Divide the first term of the dividend by the first term of the divisor:of the d

$\frac{5x^2}{x}=5x$

$\begin{gathered} \text{ }5x \\ x-1\text{ \mid }5x^2-3x+2 \end{gathered}$

Multiply 5x by the divisor: div

$5x*(x-1)=5x^2-5x$

Subtract this product from the dividend:

$\begin{gathered} \text{ }5x \\ x-1\text{ \mid }5x^2-3x+2 \\ \text{ }5x^2-5x \\ \text{ }2x+2 \end{gathered}$

Now divide 2x+2 by x = 2. Repeat the procedure:rocedurrocedu

$\begin{gathered} \text{ }5x+2 \\ x-1\text{ \mid }5x^2-3x+2 \\ \text{ }5x^2-5x \\ \text{ }2x+2 \\ \text{ }2x-2 \\ \text{ 4} \end{gathered}$

The quotient is 5x + 2 and the remainder is 4

a