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

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

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Solution 1

7 + 3x will be a factor of 3x3 + 7x only if 7 + 3x divides 3x3 + 7x leaving no remainder.

Let p(x) = 3x3 + 7x

7 + 3x = 0

⇒ 3x = -7

`⇒ x = -7/3`

`therefore"Remainder "= 3(-7/3)^3+7(-7/3)`

                        `= -343/9-49/3`

                        `= -490/9`

                        `≠ 0`

∴ 7 + 3x is not a factor of 3x3 + 7x.

Solution 2

Let us divide (3x3 + 7x) by (7 + 3x). If the remainder obtained is 0, then 7 + 3will be a factor of 3x3 + 7x.

By long division,

As the remainder is not zero, therefore, 7 + 3x is not a factor of 3x3 + 7x.

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Chapter 2: Polynomials - Exercise 2.3 [Page 40]

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NCERT Mathematics Class 9
Chapter 2 Polynomials
Exercise 2.3 | Q 3 | Page 40

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