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Coordinate Geometry
Question
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Determine which of the following polynomials has (x + 1) a factor:

x4 + x3 + x2 + x + 1

Answer

x4 + x3 + x2 + x + 1
Let p(x) = x4 + x3 + x2 + x + 1
The zero of x + 1 is - 1.
p(- 1) = (- 1)4 + (- 1)3 + (- 1)2 + (- 1) + 1
= 1 - 1 + 1 - 1 + 1 = 1 ≠ 0
∴ By factor theorem, x + 1 is not a factor of x4 + x3 + x2 + x + 1.

Sponsor Area

Some More Questions From Coordinate Geometry Chapter

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

4x2 - 3x + 7

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

x10+ y3 + t50

Write the coefficients of x2 in each of the following:

2 + x2 + x

Write the coefficients of x2 in each of the following:
2 - x2 + x3