Find Constant c...1

[nycmathguy]

Section 2.3
Question 92

Can you do 92 as a guide for me to do 91?
If synthetic division applies, use it.

 

[MathLover1]

92.

Let f(x) = x^5 - 2x^2 + x + c
For the denominator to divide numerator, then
f(-2) = 0
(-2)^5 - 2(-2)^2 - 2 + c = 0
-32 - 2(4) - 2 + c = 0
-32 - 8 - 2 + c = 0
-42 + c = 0
c = 42

The constant c = 42.

check:
f(x) = x^5 - 2x^2 + x + 42 divide by (x+2)

x^5 - 2 x^2 + x + 42 = ((x^4 - 2 x^3 + 4 x^2 - 10 x + 21))*(x + 2) + 0

 

[nycmathguy]

92.

Let f(x) = x^5 - 2x^2 + x + c
For the denominator to divide numerator, then
f(-2) = 0
(-2)^5 - 2(-2)^2 - 2 + c = 0
-32 - 2(4) - 2 + c = 0
-32 - 8 - 2 + c = 0
-42 + c = 0
c = 42

The constant c = 42.

check:
f(x) = x^5 - 2x^2 + x + 42 divide by (x+2)

x^5 - 2 x^2 + x + 42 = ((x^4 - 2 x^3 + 4 x^2 - 10 x + 21))*(x + 2) + 0

You are truly an amazing mathematician.