Question

Find the value of

c

cc so that the polynomial

p

(

x

)

p(x)p, left parenthesis, x, right parenthesis is divisible by

(

x

−

3

)

(x−3)left parenthesis, x, minus, 3, right parenthesis.

p

(

x

)

=

−

x

3

+

c

x

2

−

4

x

+

3

p(x)=−x

3

+cx

2

−4x+3

Answer 1

To find the value of c such that the polynomial p(x) = -x^3 + cx^2 - 4x + 3 is divisible by (x - 3), we need to perform polynomial division and check for the remainder.

Performing polynomial division, we divide p(x) by (x - 3):

-x^2 - 2cx - 6

____________________

x - 3 | -x^3 + cx^2 - 4x + 3

-(-x^3 + 3x^2)

________________

-2x^2 - 4x

-(-2x^2 + 6x)

________________

-10x + 3

-(-10x + 30)

________________

-27

The remainder of the division is -27. For p(x) to be divisible by (x - 3), the remainder should be zero. Therefore, we need to find the value of c such that the remainder is zero, i.e., -27 = 0.

Since -27 is not equal to zero, there is no value of c that makes p(x) divisible by (x - 3).