Question

divide x^3 + 2x^2 - 5x - 6 by x-1 using long division

Answer 1

Step by step solution :

Step 1 :

Equation at the end of step 1 :

Step 2 :

x3 - 2x2 - 5x + 6

Simplify —————————————————

x - 1

Checking for a perfect cube :

2.1 x3 - 2x2 - 5x + 6 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3 - 2x2 - 5x + 6

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -5x + 6

Group 2: x3 - 2x2

Pull out from each group separately :

Group 1: (-5x + 6) • (1) = (5x - 6) • (-1)

Group 2: (x - 2) • (x2)

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Answer 2

$\huge\red{\mathfrak{Answer}}$

$x - 1) {x}^{3} + 2 {x}^{2} - 5x - 6( {x}^{2} + 3x +10 \\ \: \: \: \: \: \: \: \: \: \: \: \: {x}^{3} - {x}^{2} \\ \: \: \: \: \: \: \: \: --------- \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {3x}^{2} - 5x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {3x}^{2} - 15x \\ \: \: \: \: \: \: \: \: \: --------- \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 10x - 6 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 10x - 6 \\ \: \: \: \: \: \: \: \: \: --------- \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4$

Therefore, x²+3x+10

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