Question

Divide : 3x(5x2 + 3x3 + 2) - (2x2 + 8-x) by (3x - 2) and check your answer.
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Answer 1

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

b^2+bc+c^2=49

c^2+ca+a^2=64

Then, find the value of

(a+b+c)² - 100 = ...

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