Divide 3x(5x+3x+2) - (2x2+8-x) by -2+3x.
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Answers
Solution :-
→ Dividend = 3x(5x + 3x³ - 2) - (2x² + 8 - x) = 9x³ + 15x² - 6x - 2x² + x - 8 = 9x³ + 13x² - 5x - 8
→ Divisor = (3x - 2)
so, dividing by long division method we get,
3x-2)9x³ + 13x² - 5x - 8(3x² + (19x/3) + (23/9)
9x³ - 6x²
19x² - 5x
19x² - 38x/3
23x/3 - 8
23x/3 - 46/9
(-26/9)
therefore,
→ Quotient = 3x² + (19x/3) + (23/9)
→ Remainder = (-26/9) .
now, we know that,
→ Dividend = Divisor * Quotient + Remainder .
putting all values we get,
→ 9x³ + 13x² - 5x - 8 = (3x - 2)[3x² + (19x/3) + (23/9)] + (-26/9)
→ 9x³ + 13x² - 5x - 8 = 9x³ + 19x² + (23x/3) - 6x² - (38x/3) - (46/9) - (26/9)
→ 9x³ + 13x² - 5x - 8 = 9x³ + 19x² - 6x² + (23x - 38x)/3 - (46 + 26)/9
→ 9x³ + 13x² - 5x - 8 = 9x³ + 13x² + (-15x/3) - (72/9)
→ 9x³ + 13x² - 5x - 8 = 9x³ + 13x² - 5x - 8
→ LHS = RHS .
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if a^2+ab+b^2=25
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3x(5x + 3x + 2) - (2x² + 8 - x)
15x² + 9x² + 6x - 2x² - 8 + x
22x² + 7x - 8
Dividend → 22x² + 8x - 8
Divisor → 3x - 2
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3x - 2) 22x² + 8x - 8 (22x/3 + 30/3
22x² - (66x/3)
+ 90x/3 - 8
90x/3 - 60/3
36/3
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