Question

if p(x)=x³-2x²+kx+5 is divided by (x-2), the remainders is 11. Find k, hence find all the ZEROES of x³+kx³+3x+1​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Let f(x) = x3 + 2 x2 + k x + 3

Remainder when f(x) is divided by

(x - 30 is f(3).

=f(3) = (3)3 + 2(3)2+ k(3) + 3 = 21

= f(3) = 27 + 18 + 3k + 3 = 21

=48 + 3k = 21

=3k = -27

=k = -9

By substituting k= -9 in x3 + 2x2 + kx – 18 we get x3 + 2x2 - 9x - 18.

Let f(x) = x3 + 2x2 -9x – 18

f(-2) = (-2)3 +2(2)2-9(2) = 0

Therefore, (x + 2) is a factor of x3 +2x2 - 9x – 18.

f(-3) = (-3)3 + 2(-3)2-9(-3)= 0

Therefore, (x + 3) is a factor of x3 +2x2 - 9x – 18.

f(3) = (3)3 + 2(3)2-9(3)-18 = 0

Therefore, (x - 3) is a factor of x3 + 2x2 - 9x - 18.

The factors of x3 + 2x2 - 9x - 18 are (x-3), (x + 3) and (x + 2).