Question

if x-3 is a factor of polynomial x³+ x²-kx + 15 then k=​

Answer 1

Given,

A polynomial p(x) = x³+ x²-kx + 15

(x-3) is a factor of the polynomial p(x).

To find,

The value of k.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If (x+a) and (x+b) are two factors of a quadratic equation p(x), then (-a) and (-b) are two roots of the given quadratic equation and p(-a) = p(-b) = 0. {Statement-1}

Now, according to the question and statement-1;

(x-3) is a factor of the given polynomial p(x)

=> the value of p(x) at x=3 is equal to 0

=> p(3) = 0

=> (3)³+ (3)²-k(3) + 15 = 0

=> 27 + 9 - 3k + 15 = 0

=> 3k = 51

=> k = 51/3

=> k = 17

Hence, the value of k is equal to 17.