Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
1. Determine which of the following polynomials has
(
x
+
1
)
(x+1)
(
x
+
1
)
a factor: (i)
x
3
+
x
2
+
x
+
1
x^{3}+x^{2}+x+1
x
3
+
x
2
+
x
+
1
(ii)
x
4
+
x
3
+
x
2
+
x
+
1
x^{4}+x^{3}+x^{2}+x+1
x
4
+
x
3
+
x
2
+
x
+
1
(iii)
x
4
+
3
x
3
+
3
x
2
+
x
+
1
x^{4}+3 x^{3}+3 x^{2}+x+1
x
4
+
3
x
3
+
3
x
2
+
x
+
1
(iv)
x
3
−
x
2
−
(
2
+
2
)
x
+
2
x^{3}-x^{2}-(2+\sqrt{2}) x+\sqrt{2}
x
3
−
x
2
−
(
2
+
2
)
x
+
2
(i)
x
3
+
x
2
+
x
+
1
x^{3}+x^{2}+x+1
x
3
+
x
2
+
x
+
1
(ii)
x
4
+
x
3
+
x
2
+
x
+
1
x^{4}+x^{3}+x^{2}+x+1
x
4
+
x
3
+
x
2
+
x
+
1
(iii)
x
4
+
3
x
3
+
3
x
2
+
x
+
1
x^{4}+3 x^{3}+3 x^{2}+x+1
x
4
+
3
x
3
+
3
x
2
+
x
+
1
(iv)
x
3
−
x
2
−
(
2
+
2
)
x
+
2
x^{3}-x^{2}-(2+\sqrt{2}) x+\sqrt{2}
x
3
−
x
2
−
(
2
+
2
)
x
+
2
Browse the problem library