Factor Theorem

Question 1

f(x)=x(power 3)-4x(power 2)+x+6=0
Find 3 roots of f(x)

Answer 1

x=-1
x=2
x=3

Question 2

Show x+3 is a factor of x(power 3)+x(power 2)-4x+6

Answer 2

0=0 true

Question 3

If 2x-1is a factor of 2x(power 3)-5x(power2)-kx+3

Answer 3

k=4

Question 4

f(x)=2x(power 3)+mx(power 2)+nx+2
x-1 and x+2 are factors of f(x)

Answer 4

m=1
n=-5

Question 5

x(power 2)+ax+b is a factor of x(power 3)+qx(power 2)+rx+s
Prove: (i) r-b=a(q-a)
(ii) s=b(q-a)

Answer 5

a+k=q
b+ka=r
bk=s