**Exercise 8.5**

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

**(i) 3x**^{2}+4x+5, x-2

^{2}+4x+5, x-2

**Solution: **

**(ii) 10x**^{2} – 7x + 8, 5x-3

^{2}– 7x + 8, 5x-3

**Solution: **

**(iii) 5y**^{3} – 6y^{2}+6y – 1, 5y – 1

^{3}– 6y

^{2}+6y – 1, 5y – 1

**Solution: **

**(iv) x**^{4} – x^{3} + 5x , x-1

^{4}– x

^{3}+ 5x , x-1

**Solution: **

**(v) v**^{4}+y^{2}, y2 – 2

^{4}+y

^{2}, y2 – 2

**Solution: **

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

**(i) x + 1, 2x**^{2} + x + 4

^{2}+ x + 4

**Solution: **

**(ii) y – 2, 3y**^{3} + 5y^{2} + 5y + 2

^{3}+ 5y

^{2}+ 5y + 2

**Solution: **

**(iii) 4x**^{2} – 4x^{4}, 4x^{4}+7x^{2}+15

^{2}– 4x

^{4}, 4x

^{4}+7x

^{2}+15

**Solution:**

**(iv) 4 – z, 3z**^{2 }– 13z + 4

^{2 }– 13z + 4

**Solution: **

**(v) y**^{4}+y^{2}, y^{2}-2

^{4}+y

^{2}, y

^{2}-2

**Solution: **

**(vi) 4y + 1, 8y**^{2}-2y +1

^{2}-2y +1