Factor x3 + x2 + x + 1 by grouping. What is the resulting expression?
Solution:
Given, the equation is x3 + x2 + x + 1
We have to find the resulting expression by grouping.
Grouping first and second terms,
x3 + x2 + x + 1 = ( x3 + x2) + (x + 1)
Taking out common term,
= x2(x + 1) + (x + 1)
= (x2 + 1) (x + 1)
Therefore, the resulting expression is (x2 + 1) (x + 1).
Summary:
Factorising x3 + x2 + x + 1 by grouping, the resulting expression is (x2 + 1) (x + 1).
Example:
Factor x4 + x3 + x2 + x by grouping. What is the resulting expression?
Solution:
Given, the equation is x4 + x3 + x2 + x
We have to find the resulting expression by grouping.
Grouping first and second terms,
x4 + x3 + x2 + x = ( x4 + x3) + (x2 + x)
Taking out common term,
= x3(x + 1) + x(x + 1)
= (x3 + x) (x + 1)
= x(x2 + 1)(x + 1)
Therefore, the resulting expression is x(x2 + 1)(x + 1).
Factor x3 + x2 + x + 1 by grouping. What is the resulting expression?
Summary:
Factorising x4 + x3 + x2 + x by grouping, the resulting expression is x(x2 + 1)(x + 1).
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