[" (v) "x^(2)+19x+60],[" (vi) "x^(2)+13x+40],[" (vii) "x^(2)-10x+24]

x^(2)-10x-24=0

x^(2)-19x+84

Without solving , comment upon the nature of roots of each of the following equations : (i) 7x^(2)-9x+2=0 (ii) 6x^(2)-13x+4=0 (iii) 25x^(2)-10x+1=0 (iv) x^(2)+2sqrt(3)x-9=0 (v) x^(2)-ax-b^(2)=0 (vi) 2x^(2)+8x+9=0

Factorise each of the following polynomials using synthetic division: (i) x^(3) -3x^(2) -10x +24 (ii) 2x^(3) -3x^(2) -3x +2 (iii) -7x +3+4x^(3) (iv) x^(3) +x^(2) -14x -24 (v) x^(2) - 7x+ 6 ( vi ) x^(3) -10x ^(2) -x+ 10

Factorize following expressions (i) x^(2)+3x-40" (ii)"x^2-3x-40" (iii)"x^(2)+5x-14 (iv) x^2-3x-4" (v)"x^2-3x-40" (vi)"3x^2-10x+8 (vii) 12x^2-x-35" (viii)"3x^2-5x-2" (ix)"3x^2-7x+4 (x) 7x^2-8x+1" (xi)"2x^2-17x+26" (xii)"3a^2-7a-6 (xiii) 14a^2+a-3

Write the coefficient of (i) x in 13x (ii) y in - 5y (iii) a in 6ab (iv) z in - 7xz (v) p in - 2 pqr (vi) y^(2) in 8xy^(2)z (vii) x^(3) in x^(3) (viii) x^(2) in -x^(2)

Check whether g(x) is a factor of p(x) by dividing the first polynomial by the second polynomial: (i) p(x) = 4x^(3) + 8x + 8x^(2) +7, g(x) =2x^(2) -x+1 , (ii) p(x) =x^(4) - 5x -2, g(x) =2-x^(2) , (iii) p(x) = 13x^(3) -19x^(2) + 12x +14, g(x) =2-2x +x^(2)

Using the Remainder Theorem, factorise each of the following completely: (i) 3x^3+2x^(2)-19x+6 (ii) 2x^(3)+x^2-13x+6 (iii) 3x^(3)+2x^2-23x-30 (iv) 4x^3+7x^2-36x-63 (v) x^3+x^2-4x-4

Factorise: x ^(2) + 13x + 40

Factorise: x ^(2) - 10x + 24