Take away $(- 3 x^{3} + 4 x^{2} - 5 x + 6)$ from $(3 x^{3} - 4 x^{2} + 5 x - 6)$

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Solution

Subtracting $- 3 x^{3} + 4 x^{2} - 5 x + 6$ from
$3 x^{3} - 4 x^{2} + 5 x - 6$

$(3 x^{3} - 4 x^{2} + 5 x - 6) -$ $(- 3 x^{3} + 4 x^{2} - 5 x + 6)$
(Multiply the minus (−) sign inside the bracket)
$= 3 x^{3} - 4 x^{2} + 5 x - 6 - (- 3 x^{3}) - (4 x^{2}) - (- 5 x) - 6$
$= 3 x^{3} - 4 x^{2} + 5 x - 6 + 3 x^{3} - 4 x^{2} + 5 x - 6$
$= (3 x^{3} + 3 x^{3}) + (- 4 x^{2} - 4 x^{2}) + (5 x + 5 x)$ $+ (- 6 - 6)$
$= (3 + 3) x^{2} + (- 4 - 4) x^{2} + (5 + 5) x + (- 12)$
$= 6 x^{3} + (- 8) x^{2} + 10 x - 12$
$= 6 x^{3} - 8 x^{2} + 10 x - 12$

Hence, the required result is $6 x^{3} - 8 x^{2} + 10 x - 12$ .

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- 3 x^{3} + 4 x^{2} - 5 x + 6

3 x^{3} - 4 x^{2} + 5 x - 6

6 x^{3} - 8 x^{2} + 10 x - 12

3 x^{3} - 4 x^{2} + 5 x - 6

x = (- 1)

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