Question

Check whether 7+3x is a factor of 3x3+7x.​

Answer 1

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7+3x = 0

⇒ 3x = −7

⇒ x = -7/3

∴Remainder:

$3(-7/3)^3+7(-7/3) = -(343/9)+(-49/3)$

$= (-343-(49)3)/9$

$= (-343-147)/9$

$= -490/9 ≠ 0$

∴7+3x is not a factor of $3x^3+7x$

Answer 2

SOLUTION:-

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Let ftx) = 3x + 7..(1)

Zero of 7+3 x is x= - 7/3

Now to check whether (7+ 3x) the

polynomial is a factor of 3x+7x, we

prove that, f(-7/3) =0, by using remainder

theorem,

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On putting x=- 7/3 in eq 1,

f(-7/3)=3(-7/3)* + 7 (=-7/3)

f-7/3)= 34-343/27) - (49/3)

f-7/3)= (343/9) - (49/3)

f(-7/3)=(-343 x3 -49 * 9)/27

f-7/3) = (-1029-441)y27

f-7/3)=-1470 /27

f(-7/3)=- 490/9

Hence,

(7+3x) is not a factor of (3x +7x).