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Long Division Method to Divide Two Polynomials

What should b...

Question

What should be added to $3 x^{2} - 2 x + 8$ to get $4 x^{2} - x + 2 ?$

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Solution

Let the polynomial that should be added be a
Given $3 x^{2} - 2 x + 8 + a = 4 x^{2} - x + 2$
$a = (4 x^{2} - x + 2) - (3 x^{2} - 2 x + 8)$
$= 4 x^{2} - 3 x^{2} - x + 2 x + 2 - 8$
$= x^{2} + x - 6$

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