MA wrote:

For what value of p is the expression 2(x*x*x)-3(x*x)+7x+p divisible by x+1 ?

i prefer to do this way: 2(x*x*x)-3(x*x)+7x+p divisible by x+1

= 2x^3 - 3x^2 + 7x + p

= 2x^3 + 2x^2 - 5x^2 - 5x + 12x + 12

(start from the begaining ==> adjust the second term accordingly so that 2x^2 is a common term from the first and second term and also make necessary adjustments accordingly so the x+1 is left from every two terms after taking a common term as above)

= 2x^2 (x+1) - 5x (x+1) + 12 (x+1)

= (x +1) (2x^2 - 5x + 12)

so P= 12.