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Question
Divide: 6x3 + 5x2 − 21x + 10 by 3x − 2
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Solution 1
6x3 + 5x2 − 21x + 10 by 3x − 2
2x2 + 3x − 5
`"3x" − "2")overline("6x"^3 + "5x"^2 − 21"x" + 10)(`
6x3 − 4x2
− +
9x2 − 21x
9x2 − 6x
− +
− 15x + 10
− 15x + 10
+ −
xxx
= 2x2 + 3x − 5
Solution 2
`(6x^3 + 5x^2 - 21x + 10)/(3x-2)`
Divide the leading term of the numerator (6x3) by the leading term of the denominator (3x): `(6x^2)/(3x) = 2x^2`
(3x − 2) × 2x2 = 6x3 − 4x2
Subtract 6x3 − 4x2 from the original numerator:
(6x3 + 5x2 − 21x + 10) − (6x3 − 4x2) = 9x2 − 21x + 10.
Divide the leading term of the new expression (9x2) by the leading term of the divisor (3x): `(9x^2)/(3x) = 3x`
(3x − 2) × 3x = 9x2 − 6x.
Subtract 9x2 − 6x from the current expression:
(9x2 − 21x + 10) − (9x2 − 6x) = −15x + 10
Divide the leading term of the new expression (−15x) by the leading term of the divisor (3x): `(-15x)/(3x) = -5`
(3x − 2) × − 5 = −15x + 10
Subtract −15x + 10 from the current expression:
(−15x + 10) − (−15x + 10) = 0.
The quotient is: 2x2 + 3x - 5
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