Polynomials

Exercise 2.3 Part 2

Question 2: Find the remainder when [`x^3 - ax^2 + 6x – a`] is divided by `x – a`.

Answer:

class nine math number system polynomial d_6

Answer: 5a


Alternate Method:

Let, `x – a = 0`
Hence, `x = a`
Substituting the value of x in given expression, we get;
`x^3 - ax^2 + 6x – a`
`= a^3 - a(a)^2 + 6a – a`
`= a^3 - a^3 + 5a= 5a`
Thus, 5a is the remainder.


Question 3: Check whether `7 + 3x` is a factor of [`3x^3 + 7x`]

Answer:

class nine math number system polynomial d_7

Since, remainder is not zero, hence `7+3x` is not a factor of [`3x^3 + 7x`]

Alternate Method:

Let, `7 + 3x = 0`
Or, `3x = 7`
Or, `x = 7/3`
Substituting the value of x in given equation, we get;
`3x^3 + 7x`
`= 3(7/3)^3 + 7 xx (7/3)`
`= 343/27 + 49/3`

Since, remainder is not zero, hence `7+3x` is not a factor of [`3x^3 + 7x`]



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