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(x^(2)-5x+6)÷(x-2)

$1$ . $\left(x^{2}-5 x+6\right) \div(x-2)$

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Divide polynomials using long division

Full solution

Q.

1

.

\left(x^{2}-5 x+6\right) \div(x-2)

Identify Polynomial and Divisor: Identify the polynomial to be divided and the divisor. $\newline$ Polynomial: $x^2 - 5x + 6$ $\newline$ Divisor: $x - 2$
Set Up Long Division: Set up the long division of $(x^2 - 5x + 6)$ by $(x - 2)$ .
Divide First Term: Divide the first term of the polynomial, $x^2$ , by the first term of the divisor, $x$ , to get $x$ . Place $x$ above the division bar.
Multiply and Subtract: Multiply the divisor $(x - 2)$ by $x$ to get $x^2 - 2x$ . $\newline$ Subtract this from the polynomial to find the remainder.
New Polynomial Division: After subtraction, the new polynomial is $-3x + 6$ . Divide the first term of the new polynomial, $-3x$ , by the first term of the divisor, $x$ , to get $-3$ . Place $-3$ above the division bar next to $x$ .
Multiply and Subtract: Multiply the divisor $(x - 2)$ by $-3$ to get $-3x + 6$ . Subtract this from the new polynomial to find the new remainder.
Division Complete: After subtraction, the remainder is $0$ . The division is complete with no remainder.

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