Find , whether or not the first polynomial is a factor of the second: `x+1,\ 2x^2+5x+4` `y-2,\ \ 3y^3+5y^2+5y+2` `

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial : x^3-3x+1,x^5-4x^3+x^2+3x+1

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial : x^2+3x+1,3x^4+5x^3-7x^2+2x+2

In each of the following find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation: 5x(5-x)=1/2 (3-x), 4-3y= (4+y)/3

Find the degree of the following polynomials 2/3 xyz^3+ 3/5 x^2 y^2 z^2 +1/2 x^3 y-y^4 z

Find the angle between the straight lines joining the origin to the point of intersection of 3x^2+5x y-3y^2+2x+3y=0 and 3x-2y=1

Find the angle between the straight lines joining the origin to the point of intersection of 3x^2+5x y-3y^2+2x+3y=0 and 3x-2y=1

Find the greatest common factor (GCF/HCF) of the following polynomials: 2x^3y^2,\ 10 x^2y^3 ,14 x y (ii) 14 x^3y^5,\ 10 x^5y^3,\ 2x^2y^2

Divide the first polynomial by the second polynomial in each of the following. Also , write the quotient and remainder: x^4-x^3+5x ,\ x-1 (ii) y^4+y^2,\ y^2,-2

Find the product of : 4x^(2) - 5y^(2) and 3x^(2) +2y^(2)

On comparing the ratios (a_1)/(a_2),(b_1)/(b_2) and (c_1)/(c_2) , find out whether the following pair of linear equations are consistent, or inconsistent. (i) 3x+2y=5; 2x-3y = 7 (ii) 2x-3y=8 ; 4x-y=9 (iii) 3/2x+5/3y=7 ; 9x-10y=14 (iv) 5x-3y=11 ; -10x+6y = -22 (v) 4/3 x +2y=8 ; 2x+3y = 12