# Plzzz help to solve this- Q. Is 3x+2 a factor of 6x(raised to the power)3+7x(raised to the power) 2-x-2. Show that DIVIDEND=DIVISOR*QUOTIENT+REMAINDER Plzzz help tomorrow is my final

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by Khushi987

2015-03-02T21:44:37+05:30

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3 x + 2 is factor of  P(x)  = 6 x³ + 7 x² - x - 2  ??

If  3 (x + 2/3)  is a factor of  the expression, P(x = - 2/3)  should be 0.
Reminder of division of P(x) by (x+2/3) is  P( - 2/3)
P(2/3) = -48/27  + 28/9 + 2/3 - 2 = 0
As the reminder is  zero,  (x + 2/3) is a factor.

Hence,  6 x³ + 7 x² - x - 2 = 3 (x + 2/3)  ( a x² + b x + c) +  0

comparing coefficients of x³ on both sides, 3 a = 6  => a = 2
coefficients of the constant terms:    -2 = 2 c    => c = -1
finding coefficient of x² term:  7 = 2 a + 3 b    =>  b = 1

quotient :  2 x² + x - 1
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3 x + 2  )  6 x³  + 7 x² - x - 2  (  2 x²  + x  - 1
6 x³  + 4 x²
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3 x² - x
3 x² + 2 x
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- 3 x - 2
- 3 x - 2
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