Question

Short Answer Type Questions (Slab-1) Using Remainder Theorem, find the remainder from (1 - 3). 1. (i) 3 - 6x2 + 9x + 3 is divided by x - 1 (ii) x3 – ax2 + 2x – a is divided by x - a (iii) 4x4 – 3x3 – 2x2 + x - 7 is divided by x - 1.​

Answer 1

Answer:

I.) Remainder is 3

2.) Remainder is a

3.) Remainder is -3

Answer 2

1)3 - 6x2 + 9x + 3 is divided by x - 1 in

Now, let's find out the zero of the linear polynomial, (x – a). This means that by remainder theorem, when x3 – ax2 + 2x – a is divided by (x – a), the remainder comes out to be f(a).

2)x3 – ax2 + 2x – a is divided by x - a

P(x) = 4x⁴ —3x³—2x² + x—7

Let P(x) is exactly divisible by (x—1) then (x—1) will be a factor of P(x) and value of x in x—1=0 will satisfy p(x)

For x—1 = 0 it gives x = 1

Now

P(1) = 4 —3–2+1–7 = —7

So, The Remainder will be —7

3)4x4 – 3x3 – 2x2 + x - 7 is divided by x - 1.