`x+8=12,` (ii) `15-x=3` and verify: `19x- "13=11x+35,`(ii) `2(x-2)-3(x-3)=5(x-5)`

Solve by cross-multiplication method. (i) 8x-3y=12,5x=2y +7 (ii) 6x+ 7y -11 =0, 5x+ 2y =13 (iii) (2)/(x)+(3)/(y) =5, (3)/(x) -(1)/(y) +9=0

Multiply: (5x+3)by(7x+2) (ii) (2x+8)by(x-3)

Verify that (-x)=x for.(i) x=(11)/(15) (ii) x=-(13)/(17)

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)

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

Solve : x^3-8x^2+19x-12=0

Verify that (- x) = x for .(i) x = (11)/(15) (ii) x = - (13)/(17)

Verify the property: x\ "x"\ y=y\ "x"\ x\ b y\ t a k ing: x=-1/3, y=2/7 (ii) x=(-3)/5, y=(-11)/(13)

Find the square root of (x^(2)-8x+15)(2x^(2)-11x+5)(2x^(2)-7x+3)