Question

can anyone help me to solve this ​no 2 and 3​

Answer 1

Question:

2. Find the remainder when x³ - ax² + 6x - a is divided by x - a.

Solution:

Let,

⟹ f(x) = x² - ax² + 6x - a

⟹ (a)³ - a×(2)² + 6×a - a

⟹ a³ - a³ + 6a - a

⟹ 6a - a

⟹ 5a

Therefore, Remainder when x³ - ax² + 6x - a is divided by x - a is 5a.

Question:

3. Check whether 7 + 3x is a factor of 3x² + 7x

Solution:

Let,

To find f(x) = 7 + 3x is a factor of g(x) = 3x² + 7x

Now,

Find the value of x from f(x) and put it into g(x). If the value is zero then it f(x) is a factor of g(x) otherwise it is not a factor.

⟹ f(x) = 7 + 3x

⟹ 3x + 7 = 0

⟹ x = - 7/3

Put the value of x in g(x).

⟹ g(x) = 3x² + 7x

⟹ g(-7/3) = 3(-7/3)² + 7(-7/3)

⟹ g(-7/3) = 3(-343/27) - 49/3

⟹ -343/9 - 49/3

⟹ -490/9

Here, g(-7/3) is not zero.

Therefore, 7 + 3x is not a factor of 3x² + 7x.