Q. 1 F5.0( 1 Vote )

# For each pair of

Given, a pair of polynomial as 3x – 1, 3x3 – 10x2 + 9x – 2

Need to find out the first polynomial is factor of second and if not a factor need to find the remainder

To check 3x – 1 is a factor of 3x3 – 10x2 + 9x – 2 we must substitute x = in the second polynomial, we get as follows

3()3 – 10()2 + 9() – 2 = – 2

= – 3 – 2

= – 5

= 0

3x – 1 is not a factor

To find the remainder divide second polynomial by first polynomial

so, we can subtract a number from the second polynomial to get the remainder

3x3 – 10x2 + 9x – 2 = (3x – 1)q(x) + c

3x3 – 10x2 + 9x – 2 –c = (3x – 1)q(x)

c = ((3x3 – 10x2 + 9x – 2) – (3x – 1)) × q(x)

Now, substitute x = in the above equation we get

= – 2 – 0

c =

is the remainder

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