Which is the quotient and remainder, written as partial fractions, of startfraction x squared 8 over x squared minus 5 x 6 endfraction?

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asked Jul 13, 2024 61.2k views

2 Answers

Martijn · Answer 1 · 2024-07-18T13:46:09+0000

To find the quotient and remainder for the division, use polynomial long division. The quotient is 1 and the remainder is 13x + 2.

To find the quotient and remainder for the division of x^2 + 8 by x^2 - 5x + 6, we can use polynomial long division.

Step 1: Divide the first term of the numerator x^2 by the first term of the denominator x^2, which gives 1 as the quotient.

Step 2: Multiply the divisor x^2 - 5x + 6 by the quotient 1, which gives x^2 - 5x + 6.

Step 3: Subtract x^2 - 5x + 6 from x^2 + 8 (numerator - (quotient * divisor)), which gives 13x + 2 as the remainder.

Therefore, the quotient is 1 and the remainder is 13x + 2, written as partial fractions.