Question

find the value of m, in order that x2-mx-2 is the quotient where x3+3x2 is divided by x+2 ?

Answer 1

Answer:

-1

Step-by-step explanation:

When x³+3x² is divided by x+2, then the quotient is x²-mx-2.

We have to find the value of m for which the above condition is true.

Now we can write that (x+2)(x²-mx-2) ≡ x³+3x² ....... (1)

We can compare the coefficients of x³, x², and x  of the above relation (1), to get the value of m.

Now, from the relation (1), we get

x³+ (2-m)x²-(m+2)x-4 ≡ x³+3x²

Now, comparing the coefficient of x² in the above relation we get,

2-m=3, ⇒ m = -1 (Answer)