Question

What must be added to x³ - 3x² - 12x + 19 so that the result is exactly divisible by x² + x - 6 ?

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Answer 1

Step-by-step explanation:

First factorise

${x}^{2} + x \: - 6 = (x \: + 3)(x \: - 2)$

Now, put x =2 in the given polynomial.

${2}^{3} - 3 \times {2}^{2} - 12 \times 2 + 19$

=

$8 - 12 - 24 + 19 = 27 - 36 = - 9$

Hence, 9 is to be added.