How do you long divide (6x^4-13x^2+x+4) by (2x^2-3)?

1 Answer
Jun 29, 2015

(6x^4 - 13x^2 +x +4)/(2x^2-3) = 3x^2 – 2 + (x-2)/(2x^2-3)

Explanation:

You use the process of long division, but you have to leave gaps for the missing powers of x.

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So,

(6x^4 - 13x^2 +x +4)/(2x^2-3) = 3x^2 – 2 + (x-2)/(2x^2-3)

Check:

(2x^2-3)( 3x^2 – 2 + (x-2)/(2x^2-3))= (2x^2-3)(3x^2-2) + x - 2

= 6x^4 - 13x^2 +6 +x - 2 = 6x^4 - 13x^2 + x + 4