Exercise 8.5

 

1. Divide the first polynomial by the second polynomial in each of the following, Also, write the quotient and remainder:

(i) 3x²+4x+5, x-2

Solution:

(ii) 10x² – 7x + 8, 5x-3

Solution:

(iii) 5y³ – 6y²+6y – 1, 5y – 1

Solution:

(iv) x⁴ – x³  + 5x , x-1

Solution:

(v) v⁴+y²,  y2 – 2

Solution:

2. Find, whether or not the first polynomials is a factor of the second:

(i) x + 1, 2x² + x + 4

Solution:

(ii) y – 2, 3y³ + 5y² + 5y + 2

Solution:

(iii) 4x² – 4x⁴, 4x⁴+7x²+15

Solution:

(iv) 4 – z, 3z² – 13z + 4

Solution:

(v) y⁴+y², y²-2

Solution:

(vi) 4y + 1, 8y²-2y +1

Solution: